The dimension of the box is 12 by 7 by 8
How to calculate the volme of a box
The volume of the box = lwh
Given the following
l = w
w = w - 5
h = w - 4
Hence;
w(w-5)(w-4) = 56w
Expand to have
(w^2-5w)(w-4) = 56w
w^3 - 4w^2 - 5w^2 + 20w = 56w
w^3 -9w^2 - 36w = 0
Factorize to get the value of w;
w(w^2-9w-36)=0
w^2 - 12w + 3w - 36 = 0
w(w-12) + 3(w-12)= 0
w = -3 and 12
Hence the dimension of the box is 12 by 7 by 8
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