Question

A Square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches.The area of the resulting rectangle is 60 in.² what was the area of the original Square?

Answer 1

Let s represent the length of any one side of the original square. The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.

The area of this rectangle is (s+9)(s-2) = 60 in^2.

This is a quadratic equation and can be solved using various methods. Let's rewrite this equation in standard form: s^2 + 7s - 18 = 60, or:

s^2 + 7s - 78 = 0. This factors as follows: (s+13)(s-6)=0, so that s = -13 and s= 6. Discard s = -13, since the side length cannot be negative. Then s = 6, and the area of the original square was 36 in^2.

Answer 2

To find the area of the original square, set up the equation (x + 9)(x - 2) = 60 and solve for x. Then, calculate the area of the original square by squaring the side length.

Step-by-step explanation:

To find the area of the original square, we need to consider the change in dimensions. Let's assume the original side length of the square was x. One side is increased by 9 inches, so the new length of one side is x + 9. The other side is decreased by 2 inches, so the new length of the other side is x - 2. The resulting rectangle has an area of 60 in².

Therefore, we can set up the equation: (x + 9)(x - 2) = 60. Expanding this equation gives us x² + 7x - 18 = 60.

Simplifying further, we get x² + 7x - 78 = 0. We can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the value of x. Once we have the value of x, we can calculate the area of the original square by squaring the side length: Area = x².

Learn more about Area of a Square