Question

two rectangles have the same perimeter 8cm. find the difference of their areas ​

Answer 1

Answer:

It is because rectangles can have different shapes. The same statement cannot be made for circles because they all have the same shape.

Consider a rectangle wider than it is tall. Now perform this surgery on it: find the horizontal mid-line and use scissors to cut along it. Now join the two pieces together by gluing the two new rectangles along a shortest edge. This gives a new rectangle with the same area (because we threw nothing away). But we have added two pieces to the perimeter each as long as the mid-line. Thus the new rectangle has a longer perimeter.