Question

use the picture to answer the next two questions. 8. write and simplify an expression to find the perimeter of the shape shown. 9. if the value of x is 3, what is the perimeter of the rectangle.

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=7x\) inches and \(w = 5\) inches.
So, \(P=2(7x + 5)\).

Step2: Simplify the expression

Using the distributive property \(a(b + c)=ab+ac\), where \(a = 2\), \(b=7x\), and \(c = 5\).
\(P=2\times7x+2\times5=14x + 10\).

Step3: Substitute \(x = 3\) into the simplified perimeter formula

When \(x = 3\), we substitute \(x\) into \(P=14x + 10\).
\(P=14\times3+10\).

Step4: Calculate the value

First, calculate \(14\times3=42\). Then, \(42+10 = 52\).

Answer:

1. The simplified expression for the perimeter is \(14x + 10\).
2. When \(x = 3\), the perimeter of the rectangle is \(52\) inches.