Questions: If the sides of a right triangle are 10 and 24, what is the length of the hypotenuse?

Solution Steps

To find the length of the hypotenuse in a right triangle when the lengths of the other two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Therefore, we can calculate the hypotenuse as \( c = \sqrt{a^2 + b^2} \).

In the given right triangle, we have the lengths of the two legs as follows:

• \( a = 10 \)
• \( b = 24 \)

According to the Pythagorean theorem, the length of the hypotenuse \( c \) can be calculated using the formula: \[ c = \sqrt{a^2 + b^2} \]

Substituting the values of \( a \) and \( b \) into the formula: \[ c = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} \] Calculating the square root gives: \[ c = 26.0 \]

Final Answer