Question

1. give the perimeter of the rectangle below in simplest form.

3x - 7, x + 2

1. solve the equation below.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). Here, the length is \( 3x - 7 \) and the width is \( x + 2 \). So we substitute these into the formula: \( P = 2[(3x - 7)+(x + 2)] \).

Step2: Simplify the expression inside the brackets

First, combine like terms inside the brackets: \( (3x - 7)+(x + 2)=3x + x- 7 + 2=4x-5 \).

Step3: Multiply by 2 to get the perimeter

Now, multiply the simplified expression by 2: \( P = 2(4x - 5)=8x-10 \).

Answer:

The perimeter of the rectangle is \( 8x - 10 \).