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

`(FK)/(KJ)=(FG)/(GH)`

`(3)/(15)=(4)/(GH)`

On cross multiplication, we get

`3* GH=4* 15`

`GH=(60)/(3)`

`GH=20`

Now,

`FH=FG+GH`

`FH=4+20`

`FH=24`

Therefore, the length of FH is 24 units.