Heron of Alexandria/Problems

Problems by Heron of Alexandria

Rectangles

Find two rectangles with integral sides, such that:

the area of the first is $3$ times the area of the second

the perimeter of the second is $3$ times the perimeter of the first.

Pythagorean Triangle

In a Pythagorean triangle, the sum of the area and the perimeter is $280$.

Find the sides and the area.