Question

Two students, Sydney and Luke, are in a disagreement about if the side lengths of 51 cm, 68 cm, and 85 cm would form a right triangle.

Sydney's argument is that yes, the side lengths 51, 68, 85 would create a right triangle and she justified with the Pythagorean Theorem.

Is Sydney's statement true or false?

Answer 1

Pythagorean theorem: In a right triangle, the square of the hypotenuse is equal to the sum of squares on the other two sides.

here we will apply the Pythagorean reciprocal (to check if the triangle is right): In a triangle, if the square of one side is equal to the sum of the squares of the other 2 sides, then this triangle is right.

51, 68, 85

if 85²=51²+68², then the lengths form a right triangle

85²=7225

68²+51²=7225

according to the Pythagorean reciprocal the triangle formed by these 3 lengths is right