Question

Using the converse the Pythagorean theorem, explain whether a triangle with sides 15, 10, 12 is a right triangle

Answer 1

To determine whether the triangle with sides of 15, 10, and 12 is a right triangle, we need to use the converse of the Pythagorean theorem.

The converse of the Pythagorean theorem states that if the square of the length of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In this case, the longest side is 15. We need to check if 15^2 is equal to the sum of the squares of the other two sides.

Calculating:
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244

Since 225 is not equal to 244, it means that the square of the longest side is not equal to the sum of the squares of the other two sides. Therefore, the triangle with sides of 15, 10, and 12 is not a right triangle.