We have that If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side.
see the attached figure
<span>If the mid point of the smaller side is ---------> x. The mid point of the larger side will be -----------> (x + 4) </span> The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8
The perimeter = 2 times the length + 2 times the width. 2(2x + 8) + 4x = 56 4x + 16 + 4x = 56 8x = 40 x = 5 Therefore length = 2x + 8 = 18cm <span>width = 2x = 10cm </span> the answer is <span>the lengths of the sides of the rectangle are </span>length = 18cm width = 10cm