Question

If a triangle has sides measuring 60, 75, and 45, is it a right triangle

No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. Yes, because 5,625 equals 5,625. Yes, because 5,625 equals 5,625. Yes, because 3,600 equals 3,600. Yes, because 3,600 equals 3,600. No, because 9,225 does not equal 2,025.

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To determine if a triangle is a right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

Let's denote the sides of the triangle as follows:
- a = 45
- b = 60
- c = 75

According to the Pythagorean theorem, if the triangle is a right triangle with the largest side being the hypotenuse, the following should be true:

a^2 + b^2 = c^2

If we plug in the values:

45^2 + 60^2 = 75^2

Calculating each side:

2025 + 3600 = 5625

5625 = 5625

Based on this calculation, the equation holds true, which means that the triangle with sides measuring 60, 75, and 45 is indeed a right triangle. So the correct statement would be:

Yes, because 5,625 equals 5,625.