Question
If a triangle has side measuring 60 in., 75 in., and 45in. in length, is it a right triangle?
Hint: Use the converse of the Pythagorean Theorem to check
answers:
No, because 9,225 does not equal to 2,025
yes, because 3,600 equals 3,600
no, because 5,625 does not equal to 3,600
yes, because 5,625 equals 5,625
Hint: Use the converse of the Pythagorean Theorem to check
answers:
No, because 9,225 does not equal to 2,025
yes, because 3,600 equals 3,600
no, because 5,625 does not equal to 3,600
yes, because 5,625 equals 5,625
Answers
GPT-4o mini
To determine whether the triangle with sides measuring 60 in., 75 in., and 45 in. is a right triangle, we can use the converse of the Pythagorean Theorem. According to this theorem, if the square of the length of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.
1. Identify the lengths of the sides:
- Side a = 45 in.
- Side b = 60 in.
- Side c = 75 in. (the longest side)
2. Calculate the squares of the side lengths:
- \( a^2 = 45^2 = 2025 \)
- \( b^2 = 60^2 = 3600 \)
- \( c^2 = 75^2 = 5625 \)
3. Check the Pythagorean condition:
- We need to check if \( c^2 = a^2 + b^2 \):
- \( 5625 = 2025 + 3600 \)
- \( 5625 = 5625\)
Since \( 5625 \) does equal \( 5625 \), this means that the triangle **is a right triangle**.
So the correct answer is:
**yes, because 5,625 equals 5,625**.
1. Identify the lengths of the sides:
- Side a = 45 in.
- Side b = 60 in.
- Side c = 75 in. (the longest side)
2. Calculate the squares of the side lengths:
- \( a^2 = 45^2 = 2025 \)
- \( b^2 = 60^2 = 3600 \)
- \( c^2 = 75^2 = 5625 \)
3. Check the Pythagorean condition:
- We need to check if \( c^2 = a^2 + b^2 \):
- \( 5625 = 2025 + 3600 \)
- \( 5625 = 5625\)
Since \( 5625 \) does equal \( 5625 \), this means that the triangle **is a right triangle**.
So the correct answer is:
**yes, because 5,625 equals 5,625**.