Question

Examine the right triangle.

bottom line is 17
side line is 48

What is the length of the hypotenuse?

(1 point)
Responses

60 cm
60 cm

4225−−−−√ cm
4225−−−−√ cm

65 cm
65 cm

2593−−−−√ cm

Answer 1

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.

In this case, one side \( a \) is 17 cm, and the other side \( b \) is 48 cm. Let's calculate the hypotenuse \( c \):

1. Calculate \( a^2 \) and \( b^2 \):

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

2. Add \( a^2 \) and \( b^2 \):

\[
a^2 + b^2 = 289 + 2304 = 2593
\]

3. Now take the square root to find \( c \):

\[
c = \sqrt{2593}
\]

Thus, the length of the hypotenuse is \(\sqrt{2593}\) cm.

The correct response is:

\[ 2593−−−−√ \text{ cm} \]