Question

A square and a rectangle have the same area. The square has side length 8 in. The length of the
rectangle is four times its width. What is the length of the rectangle?

Answer 1

The first step we take is to find the area of the square since the area of the square is equal to the area of the rectangle

       $area-of-rectangle = area- of-square\\area-of-rectangle = 8*8 = 64in^2$

Another fact we know is that the length of the rectangle is four times the width.

      L = 4W

• L: Length's length
• W: Width's length

Now let's put the variables, found above, into the format to find the area of the rectangle

  $area-of-rectangle = L * W, (L = 4W)\\area-of-rectangle = 4W * W\\\\64 = 4W^2\\16 = W^2\\\\W^2 = 16\\\\W = 4$

Since the Width is 4, L = 4 * W = 4 * 4 = 16 in.

So the length is 16 inches

Hope that helps!