Question

If a triangle has sides measuring 60, 75, and 45, is it a right triangle?
A. Yes, because 3,600 equals 3,600
B. No, because 5,625 does not equal 3,600
C. No, because 9,225 does not equal 2,025
D. Yes, because 5,625 equals 5,625

Answer 1

To determine if a triangle is a right triangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we can calculate the squares of the lengths of the sides in the given triangle:

60^2 = 3600
75^2 = 5625
45^2 = 2025

The numbers given in the options are the squares of the sides. Comparing the squares of the sides calculated from the given measurements, we find that 5625 does not equal 3600. Therefore, the triangle is not a right triangle.

Thus, the correct answer is:

C. No, because 9,225 does not equal 2,025