Question

A programmer wants to display how the shape of a rectangle with a fixed perimeter of 375 inches can be changed by varying the rectangle's length and width. Define a function g that determines the area (in square inches) of this rectangle given the rectangle's length l (in inches). g(l) = _________

Answer 1

Answer:

A = 187.5L - L^2

So,

g(l) = 187.5l - l^2

Step-by-step explanation:

The perimeter of a rectangle is given by:

P = 2(L + B)

Where P = perimeter

L = Length

B = Width

Making B the subject of formula, we have;

B = P/2 - L ......1

The area of a rectangle is:

A = L × B ........2

Substituting equation 1 to 2.

A = L × (P/2 - L)

A = LP/2 - L^2 .......3

Given that the perimeter P = 375 inches

A = L(375)/2 - L^2

A = 187.5L - L^2

So,

g(l) = 187.5l - l^2