Posted by **Piggy** on Wednesday, February 22, 2012 at 10:52pm.

The surface area of a right rectangular prism is 112 sq units. The height is twice the width. The length is 4 units more than the height . Find the volume.

- geometry -
**Reiny**, Wednesday, February 22, 2012 at 11:09pm
width --- x

length --- x+4

height --- 2x

surface area

= 2(x)(x+4) + 2(x)(2x) + 2(2x)(x+4)

= 112

2x^2 + 8x + 4x^2 + 4x^2 + 16x = 112

10x^2 + 24x - 112=0

5x^2 + 12x - 56 = 0

x = (-12 ± √1264)/10

= 2.355 or a negative

width = 2.355

length = 6.355

height = 4.711

check:

2(2.355(6.355) + 2(2.355)(4.711) + 2(6.355)(4.711) = 112

- geometry -
**Reiny**, Wednesday, February 22, 2012 at 11:10pm
volume = (2.355)(6.355)(4.711) = .....

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