To determine if a triangle with side lengths 6, 10, and 8 is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we identify the longest side (10) as the potential hypotenuse. We will compare \(10^2\) with \(6^2 + 8^2\):
-
Calculate \(10^2\):
\(10^2 = 100\) -
Calculate \(6^2 + 8^2\):
\(6^2 = 36\)
\(8^2 = 64\)
So, \(6^2 + 8^2 = 36 + 64 = 100\)
Now, we compare:
- \(6^2 + 8^2 = 100\)
- \(10^2 = 100\)
Since both expressions are equal, \(100 = 100\), this means that the triangle with sides 6, 8, and 10 does form a right triangle.
Elinor's analysis was mistaken. She incorrectly calculated and compared the squares.
Therefore, the correct response is:
No, she should've added 6 squared and 8 squared and compared that to 10 squared.