To find the length of the hypotenuse in a right triangle with legs measuring 10 cm and 24 cm, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs.
In your case, let \( a = 10 \) cm and \( b = 24 \) cm. Now substitute these values into the equation:
\[ c^2 = 10^2 + 24^2 \]
Calculating the squares:
\[ c^2 = 100 + 576 \] \[ c^2 = 676 \]
Now, take the square root of both sides to find \( c \):
\[ c = \sqrt{676} = 26 \text{ cm} \]
Therefore, the length of the hypotenuse is 26 cm.