To find the hypotenuse of a right triangle with side lengths of 10 and 12, applying the Pythagorean theorem yields the exact value of the hypotenuse as 2√61.
To find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known, we use the Pythagorean theorem, which 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).
This relationship is expressed as a² + b² = c².
Given side lengths of 10 and 12, we can set up the equation as follows:
Let a = 10
Let b = 12
Then solving for c, we have c = √(a² + b²) = √(10² + 12²)
Cleaning up the equation, we get c = √(100 + 144) = √(244).
The exact value of the hypotenuse is √(244), which can also be simplified by extracting perfect squares: c = √(4² × 61) = 2√61.