Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects

Answers

Answer 1

Answer:

Area of triangle ADC  is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]

and AD be [tex]y[/tex]

To, find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

= [tex]\frac{1}{2}(14-x)(y)[/tex]

We will have to determine [tex]x[/tex] and [tex]y[/tex]

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

For the given triangle ABC

Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA

Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]

∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]

Then,

Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]

Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]

Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]

Hence,

Area of triangle ABC =  [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

84 =   [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]

[tex]84 = 7y\\y = \frac{84}{7}[/tex]

∴ [tex]y = 12[/tex]

Hence, [tex]y =[/tex] AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = [tex]\sqrt{25}[/tex]

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

Area of triangle ADC  = [tex]\frac{1}{2} (9)(12)[/tex]

Area of triangle ADC  = 9 × 6

Area of triangle ADC  = 54 square unit

Hence, Area of triangle ADC  is 54 square unit.

Let ABC Be A Triangle Such That AB=13 BC=14 And CA=15. D Is A Point On BC Such That AD Bisects

Related Questions


Find the missing exponent

Answers

Answer:

-6

Step-by-step explanation:

When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis.  The answer is -6 because -6*2 is -12.

Hope this helps. If you have questions put them in the comments.

Answer:-6

Step-by-step explanation:

When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis. The answer is -6 because -6*2 is -12.

What is 1/5 miles in units to 1/65 hours

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Answer:

13/65 miles in 1/65 of an hour, I believe is the answer you're looking for. Hope this helped!

Step-by-step explanation:

OLGA went on an 82 mile bike trip last week by Thursday night she travel 64 miles of the total distance which president is reasonable estimate of how much of the trip OLGA completed by Thursday

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Answer:Note:  This symbol ≈ means approximately.

629 ≈ 600

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111 ≈ 100

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Now, we add the simplified numbers up: 600 + 200 + 100 + 600 = 1500. So, your answer is D or 1,500.

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Answer:

A=-8b/9

Step-by-step explanation:

What are the different types of cardinal numbers?

Answers

Answer:

Cardinal, Ordinal, and Nominal Numbers

Step-by-step explanation:

Answer:

A Cardinal Number is a number that says how many of something there are, such as one, two, three, four, five. An Ordinal Number is a number that tells the position of something in a list, such as 1st, 2nd, 3rd, 4th, 5th etc

Color of car driven:___________.Is the variable qualitative or quantitative? A. The variable is qualitative because color is found by measuring or counting. B. The variable is qualitative because color describes an attribute or characteristic. C. The variable is quantitative because color describes an attribute or characteristic. D. The variable is quantitative because color is found by measuring or counting.

Answers

Answer:

B. The variable is qualitative because color describes an attribute or characteristic.

Step-by-step explanation:

Color is a qualitative variable, used to describe an object. Color cannot be measure or counted, but can be used as a descriptive property of an object. Other examples of qualitative variables include beauty, happiness etc

Quantitative variables are those that can be counted or measure. examples of quantitative variables are height. age, weight, loudness, etc

Express the following vector in the form v vi+V2j+ v3k 3u -v if u (3,5,-8) and v (2,-5,7)

Answers

Answer:

7i+20j-31k

Step-by-step explanation:

Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;

u = 3i+5j-8k

v = 2i-5j+7k

To express the vector 3u - v in vector form, first let us find the vector 3u;

3u = 3(3i+5j-8k)

3u = 3(3i)+3(5j)-3(8k)

3u = 9i+15j-24k

Subtract v from the resulting vector.

Since v =  2i-5j+7k

3u - v = 9i+15j-24k - (2i-5j+7k)

3u-v = 9i+15j-24k -2i+5j-7k

collect the like terms

3u-v = 9i-2i+15j+5j-24k-7k

3u-v = 7i+20j-31k

Hence the vector 3u-v in the form v =  vi+V2j+ v3k is 7i+20j-31k

Which is the best estimate of 47 to the nearest tenth?i

Answers

Answer:

47.0

Step-by-step explanation:

Answer:

Square Root of 47 to the nearest tenth, means to calculate the square root of 47 where the answer should only have one number after the decimal point. To check that the answer is correct, use your calculator to confirm that 6.92 is about 47.

Step-by-step explanation:

Plz Mark me as brainliest

A woman making $3000 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. Find her salary after the raise.

Answers

Answer:

$3240 a month

Step-by-step explanation:

First, find her reduced salary:

3000(0.9)

= 2700

Then, find her salary after the raise:

2700(1.2)

= 3240

So, her salary after the raise is $3240 a month

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:
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Revenue per occupied room per night $ 75
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b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
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d. What percentage of rooms would need to be occupied, on average, to break even?

Answers

Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Monthly fixed cost= $6,000

Variable cost per occupied room per night= $20

Revenue per occupied room per night= $75

First, we need to structure the total cost formula:

Total cost= 6,000 + 20*x

x= occupied room

Now, we can find the expression for total revenue:

Revenue= selling price per unit*units - fixed cost - unitary variable cost*units

Revenue= 75*x - 6,000 - 20*x

I assume that the 12 rooms will be occupied for the 30 days:

Revenue= 75*(12*30) - 6,000 - 20*(12*30)

Revenue= $13,800

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1/6 of 24

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Answers

Answer:

1/2 of 24 = 12

1/6 of 24= 4

1/4 of 24 = 6

Step-by-step explanation:

divide

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Answers

Answer:

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Answers

Answer: 2000m/h

Step-by-step explanation:

speed = distance/time

milas distance was (2/3).(750 m) = 500 m, so her speed was (500 m)/(1/4) = 2000 m/h

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Answers

Answer:

I'm not really sure but I think its 6:36

Step-by-step explanation:

12 quarters + 18 nickels + 6 dimes = 36 coins in total

6 dimes in total

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Answers

her weekly allowance is $18
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Answers

Answer:

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Answers

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Answers

Answer:

$140

Step-by-step explanation:

If a package of gift cards has a total value of $1050, the total price for 2 gift cards will be 2×$1050 = $2100

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Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 140}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{1.9m + 14 = 2m}[/tex]

Move 2m to right hand side and change it's sign

Similarly, move 14 to left hand side and change it's sign

[tex] \dashrightarrow{ \sf{1.9m - 2m = - 14}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{ - 0.1m = - 14}}[/tex]

Divide both sides by -0.1

[tex] \dashrightarrow{ \sf{ \frac{ - 0.1m} { - 0.1} = \frac{ - 14}{ - 0.1}}} [/tex]

Calculate

[tex] \dashrightarrow{ \sf{m = 140}}[/tex]

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Best regards! :D

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Answers

Answer:

1/25   0.2   1/4

Step-by-step explanation:

1/25, 1/4 , 0.2

1/25 = 0.04

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Answers

Step-by-step explanation:

h(x) =-x-4

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Answer:

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Then we solve the equation

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Answers

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Answer:

Hey there!

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2
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Answers

Answer:

1, 81, and 121 are correct

Step-by-step explanation:

they are the only ones that do not have a decimal when squared

1=1

81=9

121=11

1, 81, and 121 are perfect squares.

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Answers

Answer:

8N - 4 border tiles.

Step-by-step explanation:

There are 4 border tiles in each corner and between  the tiles there are N-2 tiles along the 4 sides.

So the number of border tiles

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Answers

Answer:

tththtfhhtfhtfttfh

Step-by-step explanation:

tfhtfh

Answer:

0

Step-by-step explanation:

The question is asking for any number between -5 and 2, so you can choose -4, -3, -2, -1, 0, or 1

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Answers

the answer is A (4,7)

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Answers

Answer:

x + 6 = 3

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Step-by-step explanation:

x + 6 = 3

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Answers

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round 737.88 to the nearest tenth place?

Answers

Answer:

737.9

Step-by-step explanation:

8 is the hundredth place in 737.88, and 8 rounds up. So, the answer is 737.9

Answer:

737.9

Step-by-step explanation:

When we round something to the nearest ___ place, we want to look to the value to the right of it.

Since we're rounding it to the nearest tenths place, we want to look at the value to the right of it - the hundredths place.

The number in the tens place will be one more if the hundredths place is 5 or greater. It will remain the same if the hundredths place is below 5.

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