Question

Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle using the following steps:
6^2 + 10^2 = 8^2
36 + 100 = 64
136 doesn’t equal 64
Is her answer correct?
(1 point)
• No, she should've added 6^2 from 10^2 and compared that to 8^2
• Yes, she is correct.
• No, she should've added 6^2 and 8^2 and compared that to 10^2
• No, she should've added 10^2 and 8^2 and compared that to 6^2

Answer 1

To determine if a triangle with sides 6, 10, and 8 is a right triangle, we apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the longest side is 10. Therefore, we check if:

\[ 10^2 = 6^2 + 8^2 \]

Calculating gives:

\[ 10^2 = 100 \]
\[ 6^2 + 8^2 = 36 + 64 = 100 \]

Since \( 10^2 = 6^2 + 8^2 \), the triangle does indeed satisfy the Pythagorean theorem and therefore, it is a right triangle.

Elinor’s initial calculation was incorrect because she used the side lengths incorrectly:

She compared 6^2 + 10^2 with 8^2, which is not correct.

So the correct statement is:

• **No, she should've added 6^2 and 8^2 and compared that to 10^2.**