find the dimensions

Question

The length of a rectangle is 3 meters less than twice the width. If the area of the rectangle is 464 square​ meters, find the dimensions.

Answer 1

First you need to set up your variables.

l = 2w - 3

w=width

Area of rectangle= l x w, 464

w(2w - 3) = 464

w x 2w - w x 3 = 464

2w squared - 3w = 464

2w^2 - 3w = 464

2w^2 - 3w - 464 = 0

factor

(w - 16)(2w + 29) = 0

w -16 = 0

add 16 to both sides of equal sign and w =16

2w + 29 = 0

subtract 29 from both sides and then divide by 2, w = -14.5

plug both into l = 2w - 3 to see which is true for the quadratic

2(16) - 3 = 29

32 - 3 = 29

16 x 29 = 464 yes!

2(-14.5) - 3 = 29

-29 - 3 is -32 not 29

Therefore, the dimensions of the rectangle are: w = 16 and l = 29