a rectangle which is three times a long as it is wide the same perimeter as a square of area 64cm^2. what is the length of the rectangle ?

Let's solve this step by step:

1. First, let's find the side length of the square. The area of a square is found by squaring one of its sides. So, if the area is 64 cm^2, the side length of the square is the square root of 64, which is 8 cm.

2. The perimeter of a square is four times the length of one side, so the perimeter of this square is 4 * 8 = 32 cm.

3. Now, let's consider the rectangle. Let's denote the width of the rectangle as x. According to the problem, the length of the rectangle is three times the width, so it's 3x.

4. The perimeter of a rectangle is twice the sum of its length and width. So, the perimeter of the rectangle is 2 * (x + 3x) = 2 * 4x = 8x.

5. According to the problem, the perimeters of the rectangle and the square are the same. So, we can set up the equation 8x = 32.

6. Solving this equation for x gives us x = 4 cm. So, the width of the rectangle is 4 cm.

7. The length of the rectangle is three times the width, so the length is 3 * 4 = 12 cm.

So, the length of the rectangle is 12 cm.