Question

find the value of y in rectangle efgh.
h
4y - 82
e
g
3y - 59
f
y =

Explanation:

Step1: Recall rectangle properties

In a rectangle, opposite sides are equal. So, \( HE = GF \).
Given \( HE = 4y - 82 \) and \( GF = 3y - 59 \), we set them equal: \( 4y - 82 = 3y - 59 \).

Step2: Solve for y

Subtract \( 3y \) from both sides: \( 4y - 3y - 82 = 3y - 3y - 59 \), which simplifies to \( y - 82 = -59 \).
Then add 82 to both sides: \( y - 82 + 82 = -59 + 82 \), so \( y = 23 \).

Answer:

\( 23 \)