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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-example-1
User Clodal
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1 Answer

3 votes

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.

User Hotzen
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7.0k points
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