Question

youve already found that the length is 2x - 3 and
the width is x. can you use these expressions to
write the equation for the perimeter, given that the
perimeter is 72 inches?

Explanation:

Step1: Recall the perimeter formula for a rectangle

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

Step2: Substitute the length and width into the formula

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

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (2x - 3)+x = 3x - 3 \)

Step4: Multiply by 2

Now, multiply the result by 2: \( P = 2\times(3x - 3)=6x - 6 \)

Step5: Set the perimeter equal to 72

Since the perimeter is 72 inches, we set up the equation: \( 6x - 6 = 72 \)

Answer:

The equation for the perimeter is \( 6x - 6 = 72 \) (If we are just writing the equation. If we need to solve for \( x \):

Step6: Solve for \( x \)

Add 6 to both sides: \( 6x - 6 + 6 = 72 + 6 \) which simplifies to \( 6x = 78 \)
Divide both sides by 6: \( x=\frac{78}{6}=13 \)
But based on the question of writing the equation for the perimeter with perimeter 72, the equation is \( 6x - 6 = 72 \))