If the medians of a right-angled triangle, which are drawn from the vertices of the acute angles, measure 6 cm and 8 cm, find the length of the hypotenuse.

Let the legs of the right triangle be a and b, and the hypotenuse be c. The median to the hypotenuse is c divided by 2. The median drawn to leg a is given by the formula: square root of (2b squared plus 2c squared minus a squared) divided by 2, which equals 6. The median drawn to leg b is the square root of (2a squared plus 2c squared minus b squared) divided by 2, which equals 8. Using the relation that a squared plus b squared equals c squared, these two median formulas simplify to 3b squared plus a squared equals 144 and 3a squared plus b squared equals 256. Solving this system gives a squared equals 78 and b squared equals 22, so c squared equals 100. The hypotenuse c is 10 cm.

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