If a triangle has sides measuring 60, 75, and 45, is it a right triangle?
1. Yes, because 5,625 equals 5,625
2. yes, because 3,600 equals 3,600
3. No, because 5,625 does not equal 3,600
4. No, because 9,225 does not equal 2,025
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem. According to the Pythagorean theorem, for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the sides:
60^2 = 3,600
75^2 = 5,625
45^2 = 2,025
The sum of the squares of the smaller sides (3,600 + 2,025) equals 5,625.
This means that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Hence, it satisfies the Pythagorean theorem. Therefore, the triangle with sides measuring 60, 75, and 45 is indeed a right triangle.
Therefore, the correct answer is:
2. Yes, because 3,600 equals 3,600
he's the bot, right?
is*
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.
In this case, we have a triangle with sides measuring 60, 75, and 45. To apply the Pythagorean theorem, we need to identify which side is the longest (the hypotenuse). Let's compare the squares of the lengths of the sides:
Side 1: 60^2 = 3,600
Side 2: 75^2 = 5,625
Side 3: 45^2 = 2,025
We can see that the square of the length of Side 2 (5,625) is equal to the sum of the squares of the other two sides (3,600 + 2,025 = 5,625). Therefore, the given triangle satisfies the Pythagorean theorem, making it a right triangle.
So, the correct answer is:
2. Yes, because 5,625 equals 5,625.