Question

Which is the length of the hypotenuse of the triangle?

Triangle A B C. Side A C is 12 feet and side C B is 35 feet.
StartRoot 94 EndRoot ft
StartRoot 214 EndRoot ft
33 ft
37 ft

Answer 1

To find the length of the hypotenuse of triangle ABC, 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, sides AC and CB serve as the two shorter sides (a and b).

Given:
- Side AC = 12 feet (let's denote this as \(a\))
- Side CB = 35 feet (let's denote this as \(b\))

Now we can calculate the hypotenuse \(c\):

\[
c^2 = AC^2 + CB^2
\]
\[
c^2 = 12^2 + 35^2
\]
\[
c^2 = 144 + 1225
\]
\[
c^2 = 1369
\]

Now, we take the square root of both sides to find \(c\):

\[
c = \sqrt{1369} = 37 \text{ feet}
\]

Thus, the length of the hypotenuse of triangle ABC is **37 feet**.