Question

Suppose that a rectangle has a perimeter of 20 meters. Express the area A(x) of the rectangle in terms of the length x of one of its sides. A(x)=

Answer 1

Algebraic Expressions

The perimeter of a rectangle of length x and width y can be written as:

P = 2x + 2y

It's known the perimeter is 20m, thus

2x + 2y = 20

Dividing by 2:

x + y = 20

Subtracting x:

y = 20 - x

The area of a rectangle is calculated as follows:

A = x.y

Substituting the expression of y:

A(x) = x(20 - x)

Multiplying:

`A\mleft(x\mright)=20x-x^2`

This is the required expression of the area