In the figure given below CP=x+3, PA=3x+19, CQ=x and QB=3x+4 then, what value of x will make PQ || AB?

Topic:CBSE board Class 10
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In The Figure Given Below CP=x+3, PA=3x+19, CQ=x And QB=3x+4 Then, What Value Of X Will Make PQ || AB?

Answers

Answer 1

Given that

PQ || AB

CP = x+3

PA = 3x+19

DC = x+3

CA = x

QB = 3x+4

We know that

By Basic Proportionality Theorem,

CP / PA = CQ / QB

On substituting these values in the above formula

⇛ (3x+19) / (x+3) = (3x+4) / x

On applying cross multiplication then

⇛ x(3x+19) = (3x+4)(x+3)

⇛ 3x²+19x = 3x(x+3)+4(x+3)

⇛ 3x²+19x = 3x²+9x+4x+12

⇛ 3x²+19x = 3x²+13x+12

⇛ 3x²+19x-3x²-13x = 12

⇛ (3x²-3x²)+(19x-13x) = 12

⇛ 0+6x = 12

⇛ 6x = 12

⇛ x = 12/6

⇛ x = 2

∴ , x = 2

Answer: The value of x for the given problem is 2

Additional comment:

Basic Proportionality Theorem

" A line drawn parallel to the one side of a triangle intersecting other two sides at two different points, then the line divides the other two sides in the same ratio".

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Let r represent Rick’s height.Therefore, the quotient of Rick’s height and 4[tex] = \frac{r}{4} [/tex]Fred is 5 inches shorter than the quotient of Rick’s height and 4.Therefore, an expression that represents Fred’s height is [tex] \frac{r}{4} - 5 [/tex]

Answer:

[tex] \frac{r}{4} - 5[/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

r represents height of RickQuotient of r and 4 means r is divided by 4

The expression till now

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