Final answer:
To determine if a triangle is a right triangle, we can calculate the squares of the three sides and check if the sum of the squares of the two shorter sides is equal to the square of the longest side. In this case, the triangle with sides of lengths 59 centimeters, 65 centimeters, and 88 centimeters is not a right triangle.
Step-by-step explanation:
A triangle is a right triangle if it satisfies the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. To determine if a triangle is a right triangle, we can calculate the squares of the three sides and check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
In this case, the longest side is 88 centimeters, so we need to check if the sum of the squares of the other two sides (59 centimeters and 65 centimeters) is equal to the square of 88 centimeters.
Solving for the squares:
592 + 652 = 3481 + 4225 = 7706
882 = 7744
Since the sum of the squares of the shorter sides is not equal to the square of the longest side, the triangle is not a right triangle.