Question

What is the value of x? Enter your answer in the box. x = . Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 99.2 feet, G D equals 62 feet, D H equals left parenthesis x plus 2 right parenthesis feet, and E H equals 112 feet.

Answer 1

The value of x is 68 ft.

Explanation:

Given information:
`\angle GED\cong \angle DEH`

Bisector of an angle of a triangle theorem states that an angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.

In triangle FEH, ED is an angle bisector

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

`(112)/(99.2)* 62=x+2`

`70=x+2`

`70-2=x`

`68=x`

Therefore the value of x is 68 ft.

Answer 2

Corresponding sides on either side of ED are proprotional, so
.. (x+2)/112 = 62/99.2
.. x +2 = 112*62/99.2 = 70

x = 68 . . . . feet