Question

find the value of the variables in the rectangle shown below.
image of a rectangle with diagonals intersecting, labeled with 6x - 6, 4y - 20, y + 31, 4x + 12
x =
y =

Explanation:

Step1: Solve for \( x \)

In a rectangle, the diagonals are equal and bisect each other, so \( 6x - 6 = 4x + 12 \).
Subtract \( 4x \) from both sides: \( 6x - 4x - 6 = 12 \), which simplifies to \( 2x - 6 = 12 \).
Add 6 to both sides: \( 2x = 12 + 6 = 18 \).
Divide by 2: \( x = \frac{18}{2} = 9 \).

Step2: Solve for \( y \)

Also, since the diagonals bisect each other, \( y + 31 = 4y - 20 \).
Subtract \( y \) from both sides: \( 31 = 3y - 20 \).
Add 20 to both sides: \( 31 + 20 = 3y \), so \( 51 = 3y \).
Divide by 3: \( y = \frac{51}{3} = 17 \).

Answer:

\( x = 9 \), \( y = 17 \)