Given the volume of a rectangular prism is 192 and the length is four more than the width and the height is 6, what is the length

Length is 8 units

Step-by-step explanation:

Start with equation for volume of a rectangular prism

V = W*H*L

Given values are H = 6 and also that the L = W + 4, put the equation in terms of W

192 = W*6*(W+4)

192 = 6W^2+24W

Moving everything to one side yields

6W^2 + 24W -192 = 0

Divide both sides by 6 yields

W^2 + 4W -32 = 0

By factoring

(W+8) * (W-4) = 0

Values would be W = -8 or 4, since we are looking for positive values (dimensions of a prism) the value would be W = 4

From the above equation L = W + 4 = 8 units

Checking

W*H*L = 4*8*6 = 192 which was the given volume from the problem statement

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