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: 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)