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What is the width of a rectangular prism if the volume is 48 cubic meters and its length is twice its width and the height is 4 meters longer than its width?
Let the width of the rectangular prism be y
Therefore we can write all the measurements of the rectangular prism in terms of y.
width = y
length = 2y
height = y + 4
Finding the volume of the rectangular prism
y x 2y x (y + 4) = 48
2y2(y+4) = 48
y2(y+4) = 24
From this equation, we can see that y must equal 2 (22 x 6 = 24)
Therefore the width of the rectangular prism is 2m.
Note that in this question, when we got to the equation y2(y+4) = 24, we used 'guess and check' to find that y was. We purposely avoided expanding the bracket as this would have left us with a cubic to solve, which is quite difficult to solve analytically unless you already know one of its roots.
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