Answer:
Explanation:
We can write the area of the rug as:
Area = 49x^2 - 25y^2
To find possible dimensions of the rug, we need to factor the expression on the right side. We can factor out 49 and 25 to get:
Area = 49 * x^2 - 25 * y^2
Area = 7 * 7 * x^2 - 5 * 5 * y^2
So, the area of the rug can be written as the product of two binomials, each of which represents one of the side lengths.
Therefore, one possible set of dimensions for the rug is 7x and 5y, and another possible set is -7x and -5y. Note that the dimensions are related in that the width of the rug is proportional to 7x, and the length is proportional to 5y.
To make the rug a square, the sides must be equal in length. To find the value that would need to be subtracted from the longer side and added to the shorter side, we take the difference between the two possible side lengths:
7x - 5y = (7x + 5y) - 2 * 5y = (7x + 5y) - 10y
So, to make the rug a square, you would need to subtract 10y from the longer side (7x) and add 10y to the shorter side (5y). This would result in both sides being equal to (7x + 5y)/2, making the rug a square.