Question

Two of the sides of a right triangle are 8 and 6 units long. How long is the third side? Find all possible answers.

Answer 1

2
`\sqrt{7\\` and 10

Explanation:

8^2 +6^2= 64+36= 100= 10^2

`√((8^2-6^2))\\` =
`√(64-36)`=
`2√(7\\)`

Answer 2

If the two given sides are the legs of the triangle, you recognize it as a 3-4-5 triangle scaled by a factor of 2. The hypotenuse is 10 units long.

If the length 8 is the hypotenuse of the triangle, the short leg is
.. √(8^2 -6^2) = √(64 -36) = 2√7 ≈ 5.292 . . . . . units long

The possible lengths of the third side are 2√7 and 10 units.