A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.
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Correct Answer: Option B
Explanation:
\(Perimeter = 2(l + b) = 24\)
\(l + b = 12 \implies l = 12 - b\)
\(Area = (12 - b) \times b = 12b - b^{2}\)
\(\frac{\mathrm d A}{\mathrm d b} = 12 - 2b = 0\) (at maximum)
\(2b = 12 \implies b = 6\)
\(l = 12 - 6 = 6m\)
\(Perimeter = 2(l + b) = 24\)
\(l + b = 12 \implies l = 12 - b\)
\(Area = (12 - b) \times b = 12b - b^{2}\)
\(\frac{\mathrm d A}{\mathrm d b} = 12 - 2b = 0\) (at maximum)
\(2b = 12 \implies b = 6\)
\(l = 12 - 6 = 6m\)