Answer:
V = 396 cubic inches
Step-by-step explanation:
width = w; length = l; height = h; volume = V; area of smallest face = a
base units are inches
w = 2 + l
h = l - 5
Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.
a = h × l = (l - 5) × l
36 = l^2 - 5l ==> l^2 - 5l - 36 = 0
Factor ==> (l - 9) × (l + 4) = 0
l = 9 and l = -4
Since length cannot be negative, 9 is the only Real answer.
l = 9
h = l - 5 = 9 - 5 = 4
w = 2 + l = 2 + 9 = 11
Volume of rectangular prism/box is length times width times height.
V = l × w × h = 9 × 11 × 4 = 396
