In a triangle, the length of the median to the hypotenuse is half the length of the hypotenuse. What is the length of the other two sides, given that the hypotenuse is 10 cm?
Correct: D
Let's denote the length of the two sides as a and b. Using the Apollonius' theorem, which states that the sum of the squares of any two sides of a triangle equals twice the square on half the third side plus twice the square on the median bisecting the third side, we can derive the relationship between the sides. However, given the median to the hypotenuse is half the hypotenuse, this implies a right-angled triangle where a and b can be determined using Pythagoras theorem as 6 cm and 8 cm (since 6^2 + 8^2 = 10^2), hence option (a) and (c) are possible answers but without further information about which is which, we can't definitively choose between them based on the information given.