Question

A rectangle has a length of 13 feet less than 3 times its width. If the area of the rectangle is 2838 square feet, find the length of the rectangle.

Answer 1

Length = 86 feet.

Explanation:

Let the width be w feet then the length l = 3w - 13.

So we have the equation

Area = w (3w - 13) = 2838

3w^2 - 13w - 2838 = 0

w = [13 +/- √(13^2 - 4*3*-2838)] / 6

= (13 +/- √34225)/ 6

= (13 + 185)/6 , (13 - 185)/6

= 198/6, - 172/6

= 33, -28.667,

We ignore the negative.

So the length = 3*33 - 13

= 86 feet