Question

A right triangle with leg lengths of 3 and 4 has a hypotenuse of length 5. Show that a triangle with side lengths 3h, 4h, and 5h is also a right triangle. Explain your reasoning

Answer 1

Explanation:

The square of the hypotenuse in a right triangle = sum of the squares of the 2 legs. (Pythagoras theorem).

5^2 = 3^2 + 4^2

25 = 9 + 16

25 = 25

(5h)^2 = (3y)^2 + (4h)^2

25h^2 = 9^h^2 + 16h^2

25h^2 = 25h^2

- so it is a right triangle.