# geometry

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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 -

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 -

volume = (2.355)(6.355)(4.711) = .....

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