Question
Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses
No, because 193 does not equal 100.
No, because 193 does not equal 100.
There is no way to tell without an angle measure.
There is no way to tell without an angle measure.
Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
No, because 149 does not equal 144.
Responses
No, because 193 does not equal 100.
No, because 193 does not equal 100.
There is no way to tell without an angle measure.
There is no way to tell without an angle measure.
Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
No, because 149 does not equal 144.
Answers
GPT-4o mini
To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can apply the Pythagorean theorem. A triangle is a right triangle if the square of the length of the longest side (the hypotenuse) equals the sum of the squares of the lengths of the other two sides.
1. Identify the longest side. In this case, it is 12.
2. We need to check if \( 12^2 = 7^2 + 10^2 \).
Calculating the squares:
- \( 12^2 = 144 \)
- \( 7^2 = 49 \)
- \( 10^2 = 100 \)
Now, we sum the squares of the two shorter sides:
\( 7^2 + 10^2 = 49 + 100 = 149 \)
Now we compare:
- \( 12^2 = 144 \)
- \( 7^2 + 10^2 = 149 \)
Since \( 144 \neq 149 \), the triangle with sides 7, 10, and 12 cannot be a right triangle.
So the correct response is:
**No, because 149 does not equal 144.**
1. Identify the longest side. In this case, it is 12.
2. We need to check if \( 12^2 = 7^2 + 10^2 \).
Calculating the squares:
- \( 12^2 = 144 \)
- \( 7^2 = 49 \)
- \( 10^2 = 100 \)
Now, we sum the squares of the two shorter sides:
\( 7^2 + 10^2 = 49 + 100 = 149 \)
Now we compare:
- \( 12^2 = 144 \)
- \( 7^2 + 10^2 = 149 \)
Since \( 144 \neq 149 \), the triangle with sides 7, 10, and 12 cannot be a right triangle.
So the correct response is:
**No, because 149 does not equal 144.**