Question

1. find the expression that would represent the perimeter of the rectangle. (9x + 5) (4y - 6)

Explanation:

Step1: Recall perimeter formula for rectangle

The formula for the perimeter \( P \) of a rectangle is \( P = 2\times(\text{length} + \text{width}) \). Here, length is \( 9x + 5 \) and width is \( 4y - 6 \).

Step2: Substitute length and width into formula

Substitute the values into the formula: \( P = 2[(9x + 5)+(4y - 6)] \).

Step3: Simplify the expression inside the brackets

First, simplify the expression inside the brackets: \( (9x + 5)+(4y - 6)=9x + 4y + 5 - 6 = 9x + 4y - 1 \).

Step4: Multiply by 2

Now multiply the simplified expression by 2: \( P = 2(9x + 4y - 1)=18x + 8y - 2 \).

Answer:

The expression for the perimeter of the rectangle is \( 18x + 8y - 2 \).