Question

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

Answer 1

Given:

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

To find:

The length of $FH$.

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 $FJH,KG\parallel JH$.

Using BPT, we get

$\dfrac{FK}{KJ}=\dfrac{FG}{GH}$

$\dfrac{3}{15}=\dfrac{4}{GH}$

On cross multiplication, we get

$3\times GH=4\times 15$

$GH=\dfrac{60}{3}$

$GH=20$

Now,

$FH=FG+GH$

$FH=4+20$

$FH=24$

Therefore, the length of FH is 24 units.