algebra question

Question

The perimeter of a square is 140 less than its area. What is the perimeter of the square?

Answer 1

Let "x" be the side of a square.

Then the perimeter is x + x + x + x = 4x

And the area is x•x = x²

"The perimeter is 140 less than the area" means P + 140 = A so 4x + 140 = x²

The way to solve a quadratic equation is set it equal to zero and first try to factor it:If it doesn't factor, use the quadratic formula.

x² - 4x - 140 = 0

(x + 10)(x - 14) = 0

x = -10 and x = 14

It doesn't make any sense for x to be a negative number in this case so the side of the square is 14. That means the perimeter is 4•14 = 56

Answer 2

Gin

Well if the side is x, the perimeter is 4x, and the area x².

So 4x = x²-140

x²-4x-140 = 0

You can solve this by factorising into brackets (possibly) or by using the quadratic formula

Mike