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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

Respuesta :

Answer:

a. 20

b. 25

Step-by-step explanation:

Let find the side lengths of the rectangle,

We can complete the square.

[tex] {x}^{2} + 4x - 21[/tex]

[tex] {x}^{2} + 4x = 21[/tex]

[tex] {x}^{2} + 4x + 4 = 25[/tex]

[tex](x + 2) {}^{2} = 25[/tex]

[tex](x + 2) = 5[/tex]

[tex]x = - 7[/tex]

or

[tex](x + 7)[/tex]

[tex]x = 3[/tex]

or

[tex](x - 3)[/tex]

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.

[tex] {5}^{2} = 25[/tex]

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