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

Algebra ->  Pythagorean-theorem -> 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      Log On


   

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) About Me  (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..
10%5E2+=+8%5E2%2Bx%5E2 Simplify.
100-64+=+x%5E2
x%5E2+=+36 Take the square root of both sides.
x+=+6 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:
c%5E2+=+10%5E2%2B8%5E2 Evaluate.
c%5E2+=+164 Take the square root of both sides.
c+=+sqrt%28164%29 Simplify.
c+=+sqrt%284%2A41%29
c+=+2%2Asqrt%2841%29 This is III in the answer list.
So it looks like choice (D) is the answer.