Question

if the length of one leg of a right triangle is 5 and the length of the other leg is 3, then the length of the hypotenuse is:
○ $\sqrt{8}$
○ 8
○ $\sqrt{34}$

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse.

Step2: Substitute values

Here, \( a = 5 \) and \( b = 3 \). Substitute into the formula: \( c = \sqrt{5^2 + 3^2} \).

Step3: Calculate squares

\( 5^2 = 25 \) and \( 3^2 = 9 \), so \( c = \sqrt{25 + 9} \).

Step4: Sum and simplify

\( 25 + 9 = 34 \), so \( c = \sqrt{34} \).

Answer:

\(\sqrt{34}\) (the third option, i.e., the option with \(\sqrt{34}\))