Question

The sides of certain right triangles are Pythagorean triples. In some such triangles, the sum of one

of the sides of the triangle plus the hypotenuse equals 49 cm. Find the sum, in cm, of the lengths of
the third sides of all triangles that satisfy this criteria.

Answer 1

The sum of the lengths of the third sides of all triangles that satisfy this criteria is 63 cm.

Explanation:

We know that the hypotenuse + one of the sides is equal to 49. This means the hypotenuse must be less than 49.

If we look at the pythagorean triples with hypotenuse less than 49, there are 7. Out of these 7, we can only find 3 which have a side and the hypotenuse adding up to 49.

These 3 are (7, 24, 25), (20, 21, 29), and (12, 35, 37).

If we take the third side of each of the triangles and add them up, we get 7 + 21 + 35, which adds up to 63 cm.