Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.
A) Dimensions are 13 ft. by 11 ft.
B) Dimensions are 15ft. by 14 ft.
C) Dimensions are 12 ft. by 12 ft.
D) Dimensions are 10 ft. by 14 ft.
E) Dimensions are 9 ft. by 13 ft.

Question

Quizplus · Accepted Answer

Let the dimensions of the rectangle be length L and width W.
We know the area of the rectangle is 144 sq ft, so LW = 144.
To minimize the perimeter, we need to minimize (L + W).
We can rewrite this as (L + W) = L + 144/L.
Now, we can apply the AM-GM inequality:
L + (144/L) >= 2sqrt(L * 144/L) = 2*12 = 24.
This tells us that (L + W) >= 24, with equality when L = 12 and W = 12.
Therefore, the dimensions of the rectangle that minimize the perimeter are 12 ft. by 12 ft. (choice C).

Find the Dimensions of a Rectangle of Area 144 Sq