Answer:
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
