Question

If the perimeter of a square is 28 inches and the area of the square is (x2 + 4x + 4) square inches, where x is a positive number, what is the value of x?

Answer 1

Answer:

If the perimeter of a square is 28 inches and the area of the square is (x2 + 4x + 4) square inches, and x is a both a real and a positive number, then the value of x must be 5.

Step-by-step explanation:

All sides of a square are equal length.

The area of a square is the side length squared.

perimeter p, side length s, area a, and variable x.

p = 28.   s = ?   a = x^2 + 4x + 4.   x = ?

p = 28

p = 4s.

28 = 4s.

7 = s.

a = s^2.

s = 7.

a = 7^2.

a = 49.

a = x^2 + 4x + 4.

a = 49.

x^2 + 4x + 4 = 49.

factor x^2 + 4x + 4.

(x+2)(x+2) = 49.

(x+2)^2 = 49.

√ ((x+2)^2) = √49.

take positive answer.

x+2 = 7

x = 5.