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

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.