If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses
No, because 9,225 does not equal 2,025.
No, because 9,225 does not equal 2,025.
No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.
Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.
Yes, because 5,625 equals 5,625.
To determine if a triangle is a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem 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.
In this case, we have sides measuring 60, 75, and 45. We can check if this is a right triangle by squaring the lengths of each side:
60^2 = 3600
75^2 = 5625
45^2 = 2025
Notice that 3600 does equal 5625 + 2025. Therefore, this triangle is not a right triangle.
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 other two sides.
Let's apply the Pythagorean theorem to the given triangle with sides measuring 60, 75, and 45:
Checking using the Pythagorean theorem:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
The sum of the squares of the shorter sides (3600 + 2025) is indeed equal to the square of the longest side (5625). Therefore, the triangle with sides measuring 60, 75, and 45 is a right triangle.