Question

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

There is no way to tell without an angle measure
No, because 149 does not equal 144
No, because 193 does not equal 100
Yes, because it looks like a right triangle

Answer 1

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

First, identify the longest side, which in this case is 12. Then, we will check if:

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

Calculating the squares:

\[
12^2 = 144
\]
\[
7^2 = 49
\]
\[
10^2 = 100
\]

Now, add \(7^2\) and \(10^2\):

\[
49 + 100 = 149
\]

Next, we compare the two results:

\[
144 \neq 149
\]

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

Thus, the answer is **No, because 149 does not equal 144**.