Question

What is the value of x?

Answer 1

Look at the picture.

If ABC is any triangle and AD bisects (cuts in half) the angle BAC, then

`(AB)/(BD)=(AC)/(DC)`

In our triangle we have the proportion:

`(EG)/(GD)=(EH)/(DH)`

We have:

`EG=99.2\ ft\\\\GD=62\ ft\\\\EH=112\ ft\\\\DH=(x+2)\ ft`

Substitute:

`(99.2)/(62)=(112)/(x+2)\qquad\text{cross multiply}\\\\99.2(x+2)=(62)(112)\\\\99.2(x+2)=6944\qquad\text{divide both sides by 99.2}\\\\x+2=70\qquad\text{subtract 2 from both sides}\\\\\boxed{x=68\ ft}`