Question

A triangle with sides of lengths 32, 60, and 68 is a right triangle.

Answer 1

By applying the Pythagorean Theorem, we can determine that the given triangle is a right triangle with sides of lengths 32, 60, and 68.

Step-by-step explanation:

By applying the Pythagorean Theorem, we can determine if the triangle with sides of lengths 32, 60, and 68 is a right triangle.

According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's calculate:

1. Square the length of the first side: 322 = 1024
2. Square the length of the second side: 602 = 3600
3. Add the squared lengths of the sides together: 1024 + 3600 = 4624
4. Take the square root of the sum: √4624 = 68

Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, and the calculated value for the hypotenuse is equal to the given length, we can conclude that the triangle with sides of lengths 32, 60, and 68 is indeed a right triangle.