Question

if cg = w + 2 and eg = 6w - 98, find eg in rectangle cdef.

Explanation:

Step1: Set segments equal (rectangle diagonals)

In a rectangle, diagonals bisect each other, so $CG = EG$

Step2: Substitute given expressions

$w + 2 = 6w - 98$

Step3: Solve for $w$

$-5w = -100 \implies w = 20$

Step4: Calculate $EG$

$EG = 6(20) - 98 = 120 - 98 = 22$

Answer:

22