Question

Find the third side in simplest radical form Find hypotenuse
Side A = 9
Side B = 7

Answer 1

To find the hypotenuse in a right triangle when given the lengths of the two other sides, you can use the Pythagorean theorem. The theorem 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.

Given:
- Side A (\( a \)) = 9
- Side B (\( b \)) = 7

Now, substitute the values into the equation:

\[
c^2 = 9^2 + 7^2
\]

Calculating the squares:

\[
c^2 = 81 + 49
\]
\[
c^2 = 130
\]

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

\[
c = \sqrt{130}
\]

To express \( \sqrt{130} \) in simplest radical form, we can factor \( 130 \):

\[
130 = 2 \times 5 \times 13
\]

Since none of these factors are perfect squares, \( \sqrt{130} \) is already in its simplest form.

Thus, the hypotenuse is:

\[
\sqrt{130}
\]