Lenni has a rectangular garden with a length of 5x-7 and a width of x-2. Write an expression for the total perimeter in terms of x.


Lenni measured the perimeter to be 66 feet. What is the value of x? Enter a number only in the box below.

feet

P = 12x - 18, x = 7 feet

Step-by-step explanation:

We know that the formula for the perimeter of a rectangle is:

Where l is the length and w is the width. So we just substitute in for variables:

P = 2 (5x - 7) + 2 (x - 2)

We distribute by foiling:

P = 10x - 14 + 2x - 4

Then combine like terms:

P = 12x - 18

This can be further factored to 6(2x - 3) if needed.

Since we know the expression for perimeter, we can just set it equal to 66 feet, like this:

6(2x - 3) = 66

Divide both sides by 6:

2x - 3 = 11

Add 3 to both sides:

2x = 14

Divide both sides by 2:

x = 7 feet

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