If a, b, and c satisfy the equation a ^ 2 + b ^ 2 equals c ^ 2, are 2a, 2b, and 2c also the possible side lengths of a right triangle? how do you know?

Question

Identifying right triangles

Answer 1

of course; if a, b & c satisfy the Pythagorean theorem, there's a RIGHT triangle with legs a and b, and hypotenuse c.

A triangle that is formed of sides 2a, 2b & 2c is necessarily also a right triangle. Those quantities also satisfy the Pythagorean theorem. This "doubled (in lengths)" triangle is similar to the smaller one, and its area is FOUR times the area of the smaller triangle.