Question

builder is pouring a concrete slab. the dimensions of the slab are shown. the builder will place border edging around the outside of the slab. what is the length of edging needed to go around the concrete slab? write the expression in simplest form.
(3x+2) ft
(4x +3) ft
+ ____ + __ + ____
____ ft

Explanation:

Step1: Identify the shape and formula

The concrete slab is a rectangle. The perimeter \( P \) of a rectangle is given by the formula \( P = 2\times(\text{length}+\text{width}) \). Here, the length is \( (4x + 3) \) ft and the width is \( (3x + 2) \) ft.

Step2: Substitute into the perimeter formula

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

Step3: Simplify the expression inside the parentheses

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

Step4: Multiply by 2

Now, multiply the result by 2: \( P = 2\times(7x + 5)=14x + 10 \).

Alternatively, we can also calculate the perimeter by adding all four sides: \( (4x + 3)+(3x + 2)+(4x + 3)+(3x + 2) \).

Step5: Combine like terms (alternative method)

Combine the \( x \)-terms: \( 4x+3x + 4x+3x=14x \).

Combine the constant terms: \( 3 + 2+3 + 2 = 10 \).

So the perimeter is \( 14x + 10 \) ft.

Answer:

The length of edging needed is \( \boldsymbol{14x + 10} \) ft.