SOLUTION: Two sides of a right triangle are 8 and 10. Which of the following could be the length of the third side? I. 6 II. 15 III. 2 square root (41) (A) I only (B) II only (C) I

Question 331770: Two sides of a right triangle are 8 and 10. Which of the following could be the
length of the third side?
I. 6
II. 15
III. 2 square root (41)
(A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) Assume that 10 is the length of the hypotenuse and 8 is the length of one of the legs, then, using the Pythagorean theorem, you can find the length of the other leg, which we'll label x..
Simplify.

Take the square root of both sides.
This is I in the list of possible answer.
Now assume the the length of the hypotenuse is the unknown side and we'll label this c. Again using the Pythagorean theorem, we get:
Evaluate.
Take the square root of both sides.
Simplify.

This is III in the answer list.
So it looks like choice (D) is the answer.
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