Question

the dimensions of a rectangle are 9x - 9 and 10x. write the simplified expression for the rectangles perimeter.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The formula for the perimeter \( P \) of a rectangle with length \( l \) and width \( w \) is \( P = 2(l + w) \). Here, the length can be \( 9x - 9 \) and the width can be \( 10x \) (or vice versa).

Step2: Substitute the values into the formula

Substitute \( l = 9x - 9 \) and \( w = 10x \) into the formula: \( P = 2((9x - 9) + 10x) \).

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (9x - 9) + 10x = 9x + 10x - 9 = 19x - 9 \).

Step4: Multiply by 2

Now, multiply the simplified expression by 2: \( P = 2(19x - 9) = 2\times19x - 2\times9 = 38x - 18 \).

Answer:

The simplified expression for the rectangle's perimeter is \( 38x - 18 \).