Examine the right triangle.What is the length of the hypotenuse?(1 point)Responses65 cm65 cm2593−−−−√ cm2593−−−−√ cm60 cm60 cm4225−−−−√ cm

To determine the length of the hypotenuse of a right triangle, we would typically 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). The formula is:

\[ c^2 = a^2 + b^2 \]

However, you haven't provided the lengths of the other two sides of the triangle. If you have that information, I can help you calculate the hypotenuse length!

Based on the responses you provided, it appears you're selecting from various options for the length of the hypotenuse. If you could give me the lengths of the two legs of the triangle, I can confirm which of those options is correct.

17 48

Given the lengths of the two legs of the right triangle as 17 cm and 48 cm, we can use the Pythagorean theorem to find the length of the hypotenuse \( c \).

Using the formula:

\[
c^2 = a^2 + b^2
\]

Substituting the values of \( a \) and \( b \):

\[
c^2 = 17^2 + 48^2
\]

Calculating \( 17^2 \) and \( 48^2 \):

\[
17^2 = 289
\]
\[
48^2 = 2304
\]

Now, adding those together:

\[
c^2 = 289 + 2304 = 2593
\]

To find \( c \), take the square root:

\[
c = \sqrt{2593} \, \text{cm}
\]

So, the hypotenuse length is:

\[
\sqrt{2593} \, \text{cm}
\]

Among your provided options, the correct answer is:

\(\sqrt{2593}\) cm.