Final answer:
Using the Pythagorean theorem, c = √(a² + b²), and substituting the values 5 and 7 for the legs of the triangle, we find that the length of the hypotenuse is √74.
Step-by-step explanation:
The question asks for the length of the hypotenuse in a right triangle when the lengths of the legs are given as 5 and 7. To find this, we can use the Pythagorean theorem which says 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). Using the equation c = √(a² + b²), we can substitute the given lengths of the legs into the equation to get c = √(5² + 7²) which simplifies to c = √(25+49) = √74. So, the length of the hypotenuse is √74.