Two sides of a square are represented by xsquared + 8x and 5x + 28. What is the perimeter of the square?

Perimeter

= 2((x^2 + 8x) + (5x + 28))

= 2(x^2 + 13x + 28)

= 2x^2 + 26x + 56

The sides of a square are the same length...so

x² + 8x = 5x + 28      Subtract 5x from both sides.

x² + 3x = 28              Subtract 28 from both sides.

x² + 3x - 28 = 0         Factor.

(x + 7)(x - 4) = 0        Set each factor =0

x = -7    or     x = 4

 

If x = -7, the side length = (-7)² + 8(-7) = -7

But since this is the length of a side, we want a positive number, so x must = 4

 

If x = 4, the side length = 4² + 8(4) = 48

 

perimeter = 4 * side length

perimeter = 4 * 48 = 192 units