Question

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

Answer 1

a²+b² = c²

Well we know that a 3-4-5 triangle follows this rule, if a=3, b=4, c=5.

3² + 4² = 5² ⇒ 9 + 16 = 25 ⇒ 25 = 25

Now let's multiply all the sides by 2.

(3*2)² + (4*2)² = (5*2)²

6² + 8² = 10²

36 + 64 = 100

100 = 100

Therefore, 2a, 2b, and 2c are also possible length of a right triangle.