Question

A square has the same area as a rectangle whose

longer side is 2 times the length of its shorter
side. If the perimeter of the rectangle is 24, what
is the perimeter of the square?

A) 8 √2
B)16 √2
C)32 √2
D)32

Answer 1

There is no square that has the same area as the given rectangle, and we cannot find the perimeter of the square.

Step-by-step explanation:

To find the perimeter of the square, we need to find the side length of the square. We are given that the area of the square is the same as the area of the rectangle, and that the longer side of the rectangle is 2 times the length of the shorter side. Let's say the shorter side of the rectangle is x.

This means the longer side is 2x. The area of the rectangle is x * 2x = 2x². Since the area of the square is equal to the area of the rectangle, we have x² = 2x². Dividing both sides of the equation by x², we get 1 = 2.

This is not possible, so there is no solution. Therefore, there is no square that has the same area as the given rectangle, and we cannot find the perimeter of the square.