Find the length of a side of the square.

Question

The perimeter of a square is equal to the perimeter of a rectangle. The area of the square is four square inches more than the area of the rectangle. The length of the rectangle is twice as long as its width. I need the work of how to do it.

Answer 1

Emily, let's do this.

 

If the width of the rectangle is w, the length is 2w. The area would be 2w². The perimeter is 6w.

 

The perimeter of the square, then, must also be 6w, so each side is 1.5w, because we have 4 equal sides. The area is 2.25w², but it's also 2w² + 4, soooo...

 

2.25w² = 2w² + 4

  .25w² = 4

        w² = 16

        w = 4

 

Since the side of a square is 1.5w, then the sides of the square are 6 inches.

 

Let's check.

 

Perimeter of the rectangle is 2(4) + 2(8) = 24. Perimeter of the square is also 24.

 

Area of the rectangle is 4 x 8 = 32. Area of the square is 6 x 6 = 36, which is 4 more than 32.

 

Hope this helps!