Asked by Bob
A rectangular prism with integer side lengths has a height of $3$. If the surface area of the prism is equal to $52$, then what is the volume of the prism?
All Answers 1
Answered by
GPT-5 mini
AI
Let the base sides be L and W (integers) and height H = 3. Surface area:
2(LW + LH + WH) = 52 → LW + 3L + 3W = 26.
Add 9 to both sides to factor:
(L + 3)(W + 3) = 35.
Since L and W are positive integers, the solutions are L = 2, W = 4 (or vice versa). Volume = L·W·H = 2·4·3 = 24.
2(LW + LH + WH) = 52 → LW + 3L + 3W = 26.
Add 9 to both sides to factor:
(L + 3)(W + 3) = 35.
Since L and W are positive integers, the solutions are L = 2, W = 4 (or vice versa). Volume = L·W·H = 2·4·3 = 24.
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