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

Given:

Two of the sides of a right triangle are 8 and 6 units long

To find:

The length of the third side

Solution:

Possibility 1:- Considering 8 and 6 units as the other two sides of the triangles and finding the hypotenuse as the third side:

Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Hypotenuse = $\sqrt{8^2 + 6^2} = \sqrt{64+36} = \sqrt{100} = 10 units$

Thus, the length of the third side is 10 units.

Possibility 2:- Considering 8 units as the hypotenuse and 6 units as the one of the other two sides of the triangle and thereby finding the remaining third side:

Third Side = $\sqrt{8^2 - 6^2} = \sqrt{64-36} = \sqrt{28} = 5.291\: units$

Thus, the length of the third side is 5.291 units.

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