Asked by Tee
A shed is designed so that its height is 8 meters less than its width, and its length is 10 meters greater than its width. If the volume is about 1,000 cubic meters, what is the width of the shed (to the nearest meter)?
Answers
Answered by
Reiny
width = x
length = x+10
height = x-8
x(x+10)(x-8) = 1000
x(x^2 + 2x - 80) = 1000
x^3 + 2x^2 - 80x - 1000 = 0
Does not solve nicely, I used
http://www.1728.com/cubic.htm
to get x = 11.858
So to the nearest metre, the width is 12 metres
check:
width = 12
height = 4
length = 22
volume = 12x4x22 = 1056 (good enough, considering round-off)
length = x+10
height = x-8
x(x+10)(x-8) = 1000
x(x^2 + 2x - 80) = 1000
x^3 + 2x^2 - 80x - 1000 = 0
Does not solve nicely, I used
http://www.1728.com/cubic.htm
to get x = 11.858
So to the nearest metre, the width is 12 metres
check:
width = 12
height = 4
length = 22
volume = 12x4x22 = 1056 (good enough, considering round-off)
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