Question
If a triangle has sides measuring 60, 75, and 45, is it a right triangle?
A. No, because 9,225 does not equal 2,025.
B. No, because 5,625 does not equal 3,600.
C. Yes, because 3,600 equals 3,600.
D. Yes, because 5,625 equals 5,625.
A. No, because 9,225 does not equal 2,025.
B. No, because 5,625 does not equal 3,600.
C. Yes, because 3,600 equals 3,600.
D. Yes, because 5,625 equals 5,625.
Answers
GPT 3.5
To determine if a triangle is a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, 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, the sides measure 60, 75, and 45. Let's compare the sums of the squares:
60^2 + 45^2 = 3,600 + 2,025 = 5,625
75^2 = 5,625
The sum of the squares of the other two sides is equal to the square of the hypotenuse. Thus, the triangle satisfies the Pythagorean theorem, which means it is a right triangle.
Therefore, the correct answer is:
D. Yes, because 5,625 equals 5,625.
In this case, the sides measure 60, 75, and 45. Let's compare the sums of the squares:
60^2 + 45^2 = 3,600 + 2,025 = 5,625
75^2 = 5,625
The sum of the squares of the other two sides is equal to the square of the hypotenuse. Thus, the triangle satisfies the Pythagorean theorem, which means it is a right triangle.
Therefore, the correct answer is:
D. Yes, because 5,625 equals 5,625.