Question

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prom the prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. if $dh$=44.5 feet, $ef$=39 feet, and $m\angle ghf$=128°, find $ge$.
$ge=$ ____ feet

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are congruent and bisect each other, so $DH = HF = HE = HG$.

Step2: Calculate half-diagonal length

Given $DH=44.5$ feet, so $DF = 2 \times DH = 2 \times 44.5 = 89$ feet.

Step3: Relate diagonals of rectangle

Diagonals of a rectangle are equal, so $GE = DF$.

Answer:

89 feet