Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)

Answer 1

The Converse of the Pythagorean Theorem states that if the square of the length of the longest side of 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 of the triangle is 15. To determine if the triangle is a right triangle, we need to calculate the squares of the other two sides (10 and 12) and sum them up:

10^2 + 12^2 = 100 + 144 = 244

Now we compare this sum with the square of the longest side:

15^2 = 225

Since the sum of the squares of the other two sides (244) is greater than the square of the longest side (225), we can conclude that the triangle is not a right triangle based on the Converse of the Pythagorean Theorem.