Question

3 - 59. write an expression that represents the perimeter of the shape built with algebra tiles at right. then find the perimeter if x = 3 units and y = 7 units.

Explanation:

Step1: Identify side - lengths

The horizontal sides: two sides of length \(x\) and two sides of length \(y\). The vertical sides: two sides of length \(x\) and two sides of length \(y\).

Step2: Write perimeter formula

The perimeter \(P\) of the shape is the sum of all side - lengths. \(P = 4x+4y\).

Step3: Substitute values

Given \(x = 3\) and \(y = 7\), substitute into the formula: \(P=4\times3 + 4\times7\).

Step4: Calculate

First, \(4\times3=12\) and \(4\times7 = 28\). Then \(P=12 + 28=40\).

Answer:

The expression for the perimeter is \(4x + 4y\), and when \(x = 3\) and \(y = 7\), the perimeter is \(40\) units.