Question

if a triangle has sides measuring 60, 75, and 45, is it right triangle?
a. yes, because 3,600 equals 3,600
b. No, because 9,225 does not equal 2,025
c. Yes, because 5,625 equals 5,625
d. No, because 5,625 does not equal 3,600

Answer 1

To determine if the triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, for a triangle to be a right triangle, the sum of the squares of the lengths of the two shorter sides must equal the square of the length of the longest side.

In this case, the shortest side is 45, the second shortest side is 60, and the longest side is 75.

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

75^2 = 5625

The sum of the squares of the two shorter sides (2025 + 3600 = 5625) is equal to the square of the longest side (5625).

Therefore, the triangle is a right triangle.

The correct answer is: c. Yes, because 5,625 equals 5,625.