Additional Mathematics – Calculus | e-Consult
Calculus (1 questions)
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Let the length be l and the width be w. The fence consists of two lengths, three widths (the extra divider), so
2l + 3w = 100 → w = (100‑2l)/3.
The total area is A = l·w = l(100‑2l)/3 = (100l‑2l²)/3.
Differentiate: dA/dl = (100‑4l)/3. Set to zero:
100‑4l = 0 → l = 25 m.
Then w = (100‑2·25)/3 = (100‑50)/3 = 50/3 ≈ 16.67 m.
Maximum area is obtained when the garden is 25 m by 16.67 m (approximately).