Question

solve for x and y.
perimeter = 164.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is \( P = 2(x + y) \). Given \( P=164\), so \( 2(x + y)=164\). Divide both sides by 2: \(x + y=82\).

Step2: Use the given side - length relationships

We know \( y+(y + 12)=x + y\) (from the side - length markings). Simplify: \(2y+12=x + y\), then \(x=y + 12\).

Step3: Substitute \(x=y + 12\) into \(x + y=82\)

Substitute: \((y + 12)+y=82\). Combine like terms: \(2y+12 = 82\). Subtract 12 from both sides: \(2y=82 - 12=70\). Divide by 2: \(y = 35\).

Step4: Find \(x\)

Since \(x=y + 12\), substitute \(y = 35\): \(x=35+12=47\).

Answer:

\(x = 47\), \(y = 35\)