The length of a rectangle is 6 inches more than the width. The area is 27 inches. Find the width and length.

Answer 1

The formula for finding the area of a rectangle is L x W = A.

And you know that L = W + 6 (length is width plus 6).

Now you know two of the variables to plug into the first equation.

(W+6) x W = 27

Distribute the W. W^2 + 6W = 27.

Move the 27 over.

W^2 + 6W -27 = 0

Use FOIL backward to solve.

(w + 9 )(w - 3 ) == WxW = W^2 (First); -3w (Outside); 9w (Inside); 9 x -3 = -27 (Last)

Set each of those equal to 0 and solve for W.

W+9 = 0

W-3 = 0

So W either equals -9 or 3. And since you can't have a negative length, W must equal 3, and L must equal 9 (3+6). And if you check your work, 3 x 9 = 27, which is your area.