Question

Find a formula for the described function.

A rectangle has perimeter 10 m. Express the area A of the rectangle as a function of the length, L, of one of its sides.

Answer 1

The area of the rectangle is
`A=5L-L^2`.

Explanation:

The perimeter of a rectangle is

`P=2(L+W)`

where, L is length and W is width.

It is given that perimeter of a rectangle is 10m.

`10=2(L+W)`

Divide both sides by 2.

`5=L+W`

Subtract L from both sides.

`5-L=W`

Area of a rectangle is

`A=L* W`

Substitute W=(5-L) in the above formula.

`A=L* (5-L)`

`A=5L-L^2`

Therefore, the area of the rectangle is
`A=5L-L^2`.