Could 3,6,8

Question

,
and
represent the lengths of the sides of a right triangle?

Choose one • 4 points

Yes, because the sum of the squares of the legs does equal the sum of the square of the hypotenuse.

No, because the sum of the square of the legs does not equal the square of the hypotenuse.

No, because the sum of the legs does not equal the hypotenuse
Yes, because the sum of the legs does equal the hypotenuse.

Answer 1

To determine whether the sides 3, 6, and 8 can represent the lengths of the sides of 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 longest side) is equal to the sum of the squares of the lengths of the other two sides (the legs).

First, let's identify the longest side, which is 8.

Now, we will calculate the squares of the lengths:

• \(3^2 = 9\)
• \(6^2 = 36\)
• \(8^2 = 64\)

Next, we check if the sum of the squares of the two shorter sides equals the square of the longest side:

\[ 9 + 36 = 45 \]

Since \(45 \neq 64\), the condition does not hold.

Thus, the correct answer is:

No, because the sum of the squares of the legs does not equal the square of the hypotenuse.