Question

The perimeter of a rectangle is the same as the

perimeter of a square. If the area of this rectangle
is x^2 + 4x – 21 and the side lengths are integers,
find:
a. the perimeter of the rectangle
b. the area of the square

Answer 1

a. 20

b. 25

Explanation:

Let find the side lengths of the rectangle,

We can complete the square.

`{x}^(2) + 4x - 21`

`{x}^(2) + 4x = 21`

`{x}^(2) + 4x + 4 = 25`

`(x + 2) {}^(2) = 25`

`(x + 2) = 5`

`x = - 7`

or

`(x + 7)`

`x = 3`

or

`(x - 3)`

This means the perimeter of is

2 times -7 equal 14

2 times 3 equal 6

14+6=20.

The side lengths of the square is equal so each side length will measure 5.

`{5}^(2) = 25`