Find the length and width of a rectangle that has the given area and a minimum perimeter.
1. Area: 64 sq ft
2. Area: A sq. cm
2007-12-13 05:55:57 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.) 8ft by 8ft
2.) sqrt(A) cm by sqrt(A) cm
2007-12-13 05:58:53 · answer #1 · answered by Anonymous · 0⤊ 0⤋
We want to find the dimensions of a rectangle of area 64 sq ft with minimum perimeter.
Call length L, width W, perimeter P and area A (real original).
so......P = 2L + 2W;
We need to work with either Lor W, but not both. Since LW = A, where A is known, we can get rid of one of the variables in the P equation. Selecting W to work with, and L to get rid of, P= 2 (A/W) + 2W.
To see how P varies with W, we evaluate dP/dW
dP/dW = -2A/W^2 + 2 . At minimun P, dP/dW=0. So.....at this point 2A/W^2=2 or A= W^2. Given A=64, W=8, and from the area equation, L=8.
2007-12-13 14:10:51 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋
4 ft
1 cm?
2007-12-13 14:00:34 · answer #3 · answered by Pipa 1 · 0⤊ 0⤋