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

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

Answer 2

Answer:

The value of x is 68 ft.

Step-by-step 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

$\frac{EH}{EG}=\frac{DH}{GD}$

$\frac{112}{99.2}\times 62=x+2$

$70=x+2$

$70-2=x$

$68=x$

Therefore the value of x is 68 ft.