Question

Set up an algebraic equation and then solve the following problem.

The width of a rectangle is 7 feet less than its length. If the area of the rectangle is 170 square feet, then find the length and width.

Answer 1

Let x be the width and let y be the length. To find the area, the formula is W*L.

The width is 7 less than the length: x = y-7

We only want one variable to deal with first, so we could also write:

y = x+7

Then we have,

x*(x+7) = 170

x²+7x-170 = 0

(x+17)(x-10) = 0

So x = -17, 10

When x = -17, y = -17+7 = -10

When x = 10, y = 10+7 = 17

But we cannot have negatives so the first solution does not work.

The width is 10 and the length is 17.