Question
Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses
No, because 149 does not equal 144.
No, because 149 does not equal 144.
No, because 193 does not equal 100.
No, because 193 does not equal 100.
Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
There is no way to tell without an angle measure.
Responses
No, because 149 does not equal 144.
No, because 149 does not equal 144.
No, because 193 does not equal 100.
No, because 193 does not equal 100.
Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
There is no way to tell without an angle measure.
Answers
GPT-4o mini
To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with sides \(a\), \(b\), and hypotenuse \(c\), the following must hold:
\[ a^2 + b^2 = c^2 \]
We will assume the longest side (which is 12) is the hypotenuse and check if the equation holds:
1. First, calculate \(a^2 + b^2\) where \(a = 7\) and \(b = 10\):
\[
7^2 + 10^2 = 49 + 100 = 149
\]
2. Next, calculate \(c^2\) where \(c = 12\):
\[
12^2 = 144
\]
3. Now compare \(a^2 + b^2\) and \(c^2\):
\[
149 \neq 144
\]
Since \(149\) does not equal \(144\), 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.**
\[ a^2 + b^2 = c^2 \]
We will assume the longest side (which is 12) is the hypotenuse and check if the equation holds:
1. First, calculate \(a^2 + b^2\) where \(a = 7\) and \(b = 10\):
\[
7^2 + 10^2 = 49 + 100 = 149
\]
2. Next, calculate \(c^2\) where \(c = 12\):
\[
12^2 = 144
\]
3. Now compare \(a^2 + b^2\) and \(c^2\):
\[
149 \neq 144
\]
Since \(149\) does not equal \(144\), 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.**