let the length be and the with
if the perimeter of a rectangle is , we have
if its diagonal is , we have
diagonal divides rectangle into two right triangles
in one right triangle, one leg is the length , the other leg is the width
using Pythagorean theorem, we have:
....substitute and .....solve for .....simplify
=>or
since is width, go with and the other () will be the length
or calculate:
answer:
Its length is
Its width is
where length > width
