Aprogrammer wants to display how the shape of a rectangle with a fixed perimeter of 320 inches can be changed by varying the rectangle's length and width. define a function g g that determines the area (in square inches) of this rectangle given the rectangle's length l l (in inches).

g(L) = 160L - L²

Explanation:

Given

Perimeter (P) = 320 inches

Length (L) = ?

Width (W) = ?

Area (A) = Length(L) * Width (W)

P = 2(L+W) (Substitute 320 for P in this equation)

320 = 2(L+W)

320/2 = L+W

160 = L + W

From the question, we understand that our solution should be with respect to length (l)

So, we make width(W) the subject of the formula

160 - L = W

W = 160 - L

Remember that Area (A) = Length (L) * Width (W)

A = L * W (Substitute 160-L for W in this equation)

A = L * (160-L)

A = 160L - L²

The function with respect to l is thereby defined as

g(L) = 160L - L²

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