Question

use the pythagorean theorem to find the unknown side of the right triangle.
hypotenuse length =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Identify triangle sides

The right triangle has legs \( a = 2 \) and \( b = 3 \), hypotenuse \( x \).

Step2: Apply Pythagorean theorem

Pythagorean theorem: \( a^2 + b^2 = x^2 \). Substitute \( a = 2 \), \( b = 3 \):
\( 2^2 + 3^2 = x^2 \)
\( 4 + 9 = x^2 \)
\( 13 = x^2 \)

Step3: Solve for \( x \)

Take square root: \( x = \sqrt{13} \) (since length is positive).

Answer:

\(\sqrt{13}\)