A carpenter is building a rectangular room with a fixed peri

A carpenter is building a rectangular room with a fixed perimeter of 344 ft. What dimensions would yield the maximum area? What is the maximum area?

Solution

fixed perimeter of 344 ft

Let lenght and width be l, w

2l+2w = 344

l+w = 172

Now to maximise area : A = l*w

A = l( 172 -l) = 172l -l^2

Maximum area at vertex : x= -b/2a of quadratic equation ax^2 +bx +c =0

l = -172(-2*2) = 43 ft

w = 344 - 43 = 301 ft

maximum Area = 43*301 = 17243 ft^2