Question

Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses

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.
There is no way to tell without an angle measure.

No, because 193 does not equal 100.
No, because 193 does not equal 100.

No, because 149 does not equal 144.

Answer 1

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 in a right triangle with sides \(a\), \(b\), and hypotenuse \(c\), the following holds:

\[ a^2 + b^2 = c^2 \]

We'll first identify the longest side, which is 12, and we'll treat it as the potential hypotenuse. Thus, we need to check:

\[ 7^2 + 10^2 ?= 12^2 \]

Calculating the squares:

- \(7^2 = 49\)
- \(10^2 = 100\)
- \(12^2 = 144\)

Now we add \(49\) and \(100\):

\[ 49 + 100 = 149 \]

Now, we compare this with \(12^2\):

\[ 149 \neq 144 \]

Since \(149\) is not equal to \(144\), the triangle with sides 7, 10, and 12 cannot be a right triangle.

Therefore, the correct response is:

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