In the diagram of triangle FJH below, KG || JH, FK=3, KJ=15, and FG=4. What is the length of FH?

In The Diagram Of Triangle FJH Below, KG || JH, FK=3, KJ=15, And FG=4. What Is The Length Of FH?

Answers

Answer 1

Given:

In triangle [tex]FJH,KG\parallel JH, FK=3, KJ=15,\text{ and }FG=4.[/tex]

To find:

The length of [tex]FH[/tex].

Solution:

Basic proportionality theorem(BPT): If a line intersect the two sides of a triangle and parallel to third side of the triangle, then it divides the sides proportionally.

In triangle [tex]FJH,KG\parallel JH[/tex].

Using BPT, we get

[tex]\dfrac{FK}{KJ}=\dfrac{FG}{GH}[/tex]

[tex]\dfrac{3}{15}=\dfrac{4}{GH}[/tex]

On cross multiplication, we get

[tex]3\times GH=4\times 15[/tex]

[tex]GH=\dfrac{60}{3}[/tex]

[tex]GH=20[/tex]

Now,

[tex]FH=FG+GH[/tex]

[tex]FH=4+20[/tex]

[tex]FH=24[/tex]

Therefore, the length of FH is 24 units.


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