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To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the legs of the right triangle measure 10 cm and 24 cm. Let's call the length of the hypotenuse "c".
So, according to the Pythagorean theorem:
c^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
To find the length of the hypotenuse, take the square root of both sides:
c = √676
c = 26
Therefore, the length of the hypotenuse of the right triangle is 26 cm.