the length of a rectangle is 6 inches longer than a number. the width is 4 inches less than the same number . the height is 2in, if the volume of the rectangle

Question

the length of a rectangle is 6 inches longer than a number. the width is 4 inches less than the same number . the height is 2in, if the volume of the rectangle is 832 inches cubed. find the dimensions of the rectangle.

Answer 1

Let N = the number

Then L = length = N + 6 and

W= width = N - 4

H = height = 2

Volume = Height *Length * Width = H * L * W = 832

Substitute:

2(N +6)(N -4) = 832

Divide by 2 and then expand the binomial product

N² + 2N - 24 = 416

N² + 2N - 440 = 0

Factor:

(N + 22)(N - 20) = 0

The negative root is extraneous and N = 20

L = 20 + 6 = 26 and

W = 20 - 4 = 16

Take these answers and make sure they give you the correct vlume.