Question

1. the length of a cement pad on a playground is 3 m longer than the width. the width is 5x m.

a) write an expression for the area of the cement pad.
b) if x = 2 m, what is the area of the cement pad?

Explanation:

Part (a)

Step1: Determine length expression

Width is \( 5x \) m, length is 3 m longer than width, so length \( = 5x + 3 \) m.

Step2: Area formula for rectangle

Area of rectangle \( = \text{length} \times \text{width} \). Substitute length and width: \( \text{Area} = (5x + 3)(5x) \).

Step3: Expand the expression

Using distributive property: \( (5x + 3)(5x) = 5x \times 5x + 3 \times 5x = 25x^2 + 15x \).

Step1: Substitute \( x = 2 \) into area expression

From part (a), area \( = 25x^2 + 15x \). Substitute \( x = 2 \): \( 25(2)^2 + 15(2) \).

Step2: Calculate each term

First term: \( 25(2)^2 = 25 \times 4 = 100 \). Second term: \( 15(2) = 30 \).

Step3: Sum the terms

Add the two results: \( 100 + 30 = 130 \).

Answer:

The expression for the area is \( 25x^2 + 15x \) square meters.

Part (b)