The Length of a rectangle

Question

The length of a rectangle is 9 more than the width. The area is 286 sq inches. Find the length and width

Answer 1

The area of a rectangle is found by multiplying the length times the width, or LW=A. Knowing this formula and the information given we can come up with two equations.

L = W + 9 (the length is 9 more than the width)

LW = 286 (the area is 286)

From there, we can plug in (W + 9) for L in the second equation and solve for W.

(W + 9)W = 286

W² + 9W = 286 (distributive property)

W² + 9W - 286 = 0 (subtract 286 from both sides)

(W - 13) (W + 22) = 0 (factor the polynomial)

W = 13 or W = -22 (find the zeroes)

We end up with 2 numbers, 13 and -22. But since this is a problem about length measurements, we cannot have a negative number, so we are left with W = 13. To find L, simply plug 13 into the first equation.

L = 13 + 9

L = 22

So, our rectangle has a length of 22 and a width of 13.