The length of a rectangle is 6 inches shorter than the width. the parimeter of the rectangle it's 32 inches. what is the length of the rectangle?

The formula for perimeter of a rectangle is 2l + 2w 

We know the length is 6 inches shorter than the width so we can put this as
w - 6

Now, plug this into the expression 2l + 2w and set it equal to 32

2(w - 6) + 2(w) = 32

Now solve for w

2(w - 6) + 2(w) = 32
2w - 12 + 2w = 32
4w - 12 = 32
4w = 44
w = 11

The width equals 11 inches. Now to find the length, we have to subtract 6 since it is 6 inches shorter than the width

11 - 6 = 5

The length equals 5 inches

Now plug values of the length and width back into the equation 2l + 2w = 32 to make sure

2(5) + 2(11) = 32
10 + 22 = 32
32 = 32

Since 32 equals 32, we can be sure that the length equals 5 inches and the width equals 10 inches

Hope this helped!