Question

1. write and simplify the perimeter of a rectangle with the length of (4x - 3)cm and the width of (5x)cm. 1 mark

Explanation:

Step1: Recall the perimeter formula for a rectangle

The formula for the perimeter \( P \) of a rectangle is \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( (4x - 3) \) cm and the width is \( (5x) \) cm.

Step2: Substitute the length and width into the formula

Substitute length \( = 4x - 3 \) and width \( = 5x \) into the formula: \( P = 2\times((4x - 3) + 5x) \).

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (4x - 3) + 5x = 4x + 5x - 3 = 9x - 3 \).

Step4: Multiply by 2

Now, multiply the result by 2: \( P = 2\times(9x - 3) = 2\times9x - 2\times3 = 18x - 6 \).

Answer:

The perimeter of the rectangle is \( (18x - 6) \) cm.