alleryTo find the dimensions of a rectangle with maximum area + perimeter 20, set up:
AMaximise A = xy with x + y = 20 (perimeter as sum)
BMaximise A = 2x × 2y with no constraint
CMaximise A = xy with x + y = 10 (half perimeter)
DMaximise A = x² with x + y = 10 fixed
Answer & Solution
Correct answer: C. Maximise A = xy with x + y = 10 (half perimeter)
Perimeter = 2x + 2y = 20
→ x + y = 10. Maximise A = xy = x(10−x) = 10x − x².
dA/dx = 10 − 2x = 0 at x = 5, y = 5. Square gives max area = 25 sq units.
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