The perimeter of rectangle Y is equal to its area. Rectangle Z has the same perimeter as rectangle Y. The length of rectangle Z is 5 inches an the width is 3 inches. Explain how you can find the length and width of rectangle Y.
To find the length and width of rectangle Y, we know that its perimeter equals its area. Let's denote the length of rectangle Y as 'L' and the width as 'W'.
Perimeter of rectangle Y = 2(L + W)
Area of rectangle Y = L * W
Given that the perimeter of rectangle Y is equal to its area, we can equate the two expressions and solve for L and W.
2(L + W) = L * W
We also know that rectangle Z has the same perimeter as rectangle Y. The length of Z is 5 inches, and the width is 3 inches. Therefore, we can substitute L = 5 and W = 3 into the equation.
2(5 + 3) = 5 * 3
Simplifying:
2(8) = 15
16 = 15
Since this equation is not true, it means that our assumption that the perimeter of rectangle Y is equal to its area is incorrect.
Hence, there is no unique solution to find the length and width of rectangle Y based on the given information.