Question 1130353
2L + 2W = 56
Since the house forms one side:
2L + W = 56 (you can take out one Length or one Width, it doesn't matter)
W = 56 - 2L We'll use this value for W below.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
L*W = Area (substitute for W):
L*(56-2L)= Area
56L - 2L^2 = Area
now let's call Area y and the length x and rewrite, so we have:
y = -2x^2 + 56x
x = -(b/2a) in this formula for the axis of symmetry, our a = -2 and our b = 56:
x = -56/(2(-2))
x = 14
F(14) = -2(14)^2+56(14)
F(14} = -392 + 784
F(14) = 392 this is the maximum area we can get
L = 56-2(14)
L = 56-28
L = 28
The largest total area that can be enclosed will be 14 feet wide and 28 feet long, giving a total area of 28*14 = 392 square feet