Question

quadrilateral fghi is a rectangle, ef = 12y + 22, and eg = 2y + 32. what is gi?

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal and bisect each other. So $EF = EG$.
$12y + 22=2y + 32$

Step2: Solve for y

Subtract $2y$ from both sides: $12y-2y + 22=2y-2y + 32$, which simplifies to $10y+22 = 32$. Then subtract 22 from both sides: $10y+22 - 22=32 - 22$, getting $10y=10$. Divide both sides by 10: $y = 1$.

Step3: Find length of $GI$

Since $GI = 2EG$ (diagonals bisect each other), and $EG=2y + 32$, substitute $y = 1$ into the formula for $EG$. $EG=2\times1+32=34$. Then $GI = 2\times34 = 68$.

Answer:

68