Question

An architect needs to design a rectangular room with an area of 77ft^2. What dimensions should he use in order to minimize the perimeter?

I keep getting stuck on this problem. I know when I take square root of 77, it gives me 8.77. But how do I get there.

xy= 77, y= 77/x

P= 2x+2y, P= 2x+2(77/x), P'= 2+154/x

then I have x^2= 154/2

Answer 1

you have
P = 2 x + 154/x
BUT you took the derivative incorrectly
P' = 2 -154/x^2
so
for min or max
0 = 2 - 154/x^2
or
x^2 = 77

NOTE d/dx (1/x) = -1/x^2

Answer 2

Use units and you need L times W