Question

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

Answer 1

If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses Yes, because 5,625 equals 5,625. Yes, because 5,625 equals 5,625. No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. No, because 9,225 does not equal 2,025. No, because 9,225 does not equal 2,025. Yes, because 3,600 equals 3,600.

Answer 2

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 is equal to the sum of the squares of the lengths of the other two sides.

If we label the sides of the triangle as follows:
- a = 60
- b = 75
- c = 45 (hypotenuse)

We can test whether this triangle is right-angled:
Using the Pythagorean Theorem,
a² + b² = c²

(60)² + (75)² = (45)²
3600 + 5625 = 2025 + 3600
9225 = 5625 + 3600
9225 = 9225

The equation is true, which means that the given triangle is a right triangle.