A rectangle has a perimeter of 24m. If its area is to be maximum, find...
FURTHER MATHEMATICS
WAEC 2008
A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.
- A. 12, 12
- B. 6, 6
- C. 4, 8
- D. 9, 3
Correct Answer: B. 6, 6
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)
\(2b = 12 \implies b = 6\)
\(l = 12 - 6 = 6m\)
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