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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.

Respuesta :

Answer:

Length = 86 feet.

Step-by-step 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

   

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