Question

What is the measure of the hypotenuse of a right triangle if the measures of the two sides are nine inches and forty inches?

Answer 1

hypotenuse = 41 inches

Step-by-step explanation:

using Pythagoras' identity in the right triangle

c² = a² + b²

c is the hypotenuse and a, b are the sides (legs of the triangle )

given a = 9 and b = 40 , then

c² = 9² + 40² = 81 + 1600 = 1681 ( take square root of both sides )

`√(c^2)` =
`√(1681)`

c = 41

The hypotenuse is 41 inches

Answer 2

To find the hypotenuse of a right triangle with sides measuring nine inches and forty inches, apply the Pythagorean theorem. The calculation yields a hypotenuse measuring 41 inches.

Step-by-step explanation:

The measure of the hypotenuse of a right triangle when the measures of the two sides are nine inches and forty inches can be calculated using 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). The formula is a² + b² = c²

For the given sides of 9 inches and 40 inches, we substitute these values into the formula:

9² + 40² = c²

81 + 1600 = c²

1681 = c²

Taking the square root of both sides gives us the length of the hypotenuse:

c = √1681

c = 41 inches

The hypotenuse measures 41 inches.