Two sides of a right triangle measure 10 m and 8 m. Explain why this is not enough information to be sure of the length of the third side. Give two possible values for the length of the third side.

Answer 1

You said it was a right triangle, assuming you meant
right-angled triangle.
You are given 2 sides, but did not state which two sides.
Clearly the hypotenuse has to be the longest side.

case 1: 10 m is the hypotenuse, then
a^2 + 8^2 = 10^2
a^2 = 100-64 = 36
a = 6, the 3 sides are 6, 8, and 10 (multiples of the standard 3-4-5 right-angled triangle)

case 2. the two given sides are the sides containing the 90° angle
c^2 = 10^2 + 8^2 = 164
c = √164 = 2√41 , the 3 sides are 8, 10 and 2√41