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.
Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.
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.
To determine if a triangle is a right triangle, you 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.
For the given triangle with sides measuring 60, 75, and 45, we can check if it satisfies this condition. First, let's identify the longest side.
Comparing the side lengths, we see that 75 is the longest side. Now, we can apply the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the two shorter sides, and c is the longest side (the hypotenuse).
In this case, let's take a = 60 and b = 45. Plugging these values into the equation:
60^2 + 45^2 = 75^2
Simplifying:
3600 + 2025 = 5625
So, the equation becomes:
5625 = 5625
The equation is true, which means that the given triangle satisfies the Pythagorean theorem. Therefore, the triangle with sides measuring 60, 75, and 45 is a right triangle.
So, the correct response is:
Yes, because 5,625 equals 5,625.
To determine if a triangle is a right triangle, we need to check if the square of the length of one side is equal to the sum of the squares of the other two sides. Let's calculate:
45^2 + 60^2 = 2025 + 3600 = 5625
75^2 = 5625
Since 5625 is equal to 5625, we can say that the triangle with sides measuring 60, 75, and 45 is a right triangle. Therefore, the correct response is:
Yes, because 5,625 equals 5,625.