Question

quadrilateral defg is a rectangle, df = 3v + 22, and eg = 5v - 66. what is eg? eg = \boxed{}

Explanation:

Step1: Set diagonals equal

In a rectangle, diagonals are congruent, so $DF = EG$.
$3v + 22 = 5v - 66$

Step2: Solve for $v$

Rearrange to isolate $v$ terms.
$22 + 66 = 5v - 3v$
$88 = 2v$
$v = \frac{88}{2} = 44$

Step3: Calculate $EG$

Substitute $v=44$ into $EG=5v-66$.
$EG = 5(44) - 66 = 220 - 66$

Answer:

$154$