Question

in rectangle fghi, diagonals fh and gi intersect at e.
ie = 3x+4
eg = 5x-6
what is the length of fh ?

Explanation:

Step1: Set equal segments

Diagonals of rectangle bisect each other, so \( IE = EG \).
\( 3x + 4 = 5x - 6 \)

Step2: Solve for x

Rearrange terms: \( 4 + 6 = 5x - 3x \)
\( 10 = 2x \) → \( x = 5 \)

Step3: Find FH length

FH = 2×IE (diagonal bisected). Substitute x=5:
IE = \( 3(5) + 4 = 19 \)
FH = \( 2×19 = 38 \)

Answer:

38