Question

perimeter = 164. solve for x and y.

Explanation:

Step1: Use the perimeter formula for a parallelogram

The perimeter \( P \) of a parallelogram is \( P = 2(a + b) \), where \( a\) and \( b\) are the side lengths. Here, \( a=y + 12\), \( b = y\), and \( P=164\). So, \( 164=2((y + 12)+y)\).

Step2: Simplify the equation

First, divide both sides by 2: \( \frac{164}{2}=(y + 12)+y\), which gives \( 82 = 2y+12\).
Then, subtract 12 from both sides: \( 82-12 = 2y\), so \( 70 = 2y\).
Finally, divide by 2: \( y=\frac{70}{2}=35\).

Step3: Find the value of \( x\)

In a parallelogram, opposite sides are equal. So \( x = 81\).

Answer:

\( x = 81\)