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Answer:
Volume = 480 cubic inches
Explanation:
We have the following relationships to work with
width w = h -3
length l = h + 4
area of base of prism a = l x w = 60 (1)
area of base in terms of h = (h-3)(h+4) =h² -3h + 4h -12 (2)
Setting (1) = (2) gives
h² + h -12 =60
h² + h -72 = 0
Factoring the LHS we get
(h+9)(h-8) = 0
The solutions for h are
h + 9 = 0 ==> h = -9
h - 8 = 0 ==> h = 8
Since h cannot be negative, h = 8 inches
Volume = base area x h = 60 x 8 = 480 cubic inches
Note
We do not have to calculate length and width separately, but if so,
w = 8 -3 = 5
l = 8 + 4 = 12