Question

A rectangle has perimeter 16 m. Express the area A (in m2) of the rectangle as a function of the length, L, of one of its sides.

Answer 1

The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

What is the perimeter of a rectangle?

The perimeter of a rectangle is P = 2(L + W) where

• L = length of the rectangle and
• W = width of the rectangle

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

What is the area of the rectangle?

The area of the rectangle, A = LW where

• L = length of the rectangle and
• W = width of the rectangle

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

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