To determine if a triangle with side lengths 6, 10, and 8 is a right triangle, we need to check the Pythagorean theorem, which states that for a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
In this case, the sides are:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 10 \)
Here, 10 is the longest side, so we compare:
\[ a^2 + b^2 \stackrel{?}{=} c^2 \]
Calculating these,
\[ 6^2 + 8^2 = 36 + 64 = 100 \] \[ 10^2 = 100 \]
Since \( 100 = 100 \), the triangle does indeed form a right triangle.
Elinor's calculation of \( 6^2 + 10^2 \) and comparing it to \( 8^2 \) was incorrect, because she did not use the longest side (10) as the hypotenuse for the comparison needed to establish if it was a right triangle.
Therefore, the correct response is:
No, she should've added 6 squared and 8 squared and compared that to 10 squared.