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.

No, because 149 does not equal 144.
No, because 149 does not equal 144.

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.

Answer 1

To determine if a triangle with sides of 7, 10, and 12 can be a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Here, the sides are 7, 10, and 12. First, we identify the longest side, which is 12. We then calculate whether the Pythagorean theorem holds:

1. Calculate \(12^2\):
\[
12^2 = 144
\]

2. Calculate \(7^2 + 10^2\):
\[
7^2 = 49
\]
\[
10^2 = 100
\]
\[
7^2 + 10^2 = 49 + 100 = 149
\]

Now we compare \(12^2\) with \(7^2 + 10^2\):
\[
144 \neq 149
\]

Since \(12^2\) (144) does not equal \(7^2 + 10^2\) (149), the triangle with sides 7, 10, and 12 cannot be a right triangle.

The correct response is:
**No, because 149 does not equal 144.**