Question

A right triangle has the side measurements of 15 cm and 12 cm. What is the length for the third side?

Answer 1

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

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

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

Assuming the longest side is the hypotenuse, we can identify the given sides as \(a = 12\) cm and \(b = 15\) cm. Now we can use the theorem to find \(c\):

\[
12^2 + 15^2 = c^2
\]

Calculating the squares:

\[
144 + 225 = c^2
\]

Now, adding the results:

\[
369 = c^2
\]

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

\[
c = \sqrt{369} \approx 19.2 \text{ cm}
\]

Thus, the length of the hypotenuse (third side) is approximately 19.2 cm.

If you meant for one of the given sides to be the hypotenuse instead, let's assume the 15 cm side is the hypotenuse and 12 cm is one of the legs. In that case, we would find the length of the other side \(b\) using:

\[
15^2 = 12^2 + b^2
\]

Calculating:

\[
225 = 144 + b^2
\]

This simplifies to:

\[
b^2 = 225 - 144 = 81
\]

Taking the square root gives:

\[
b = \sqrt{81} = 9 \text{ cm}
\]

So, if 15 cm is the hypotenuse, the length of the third side is 9 cm.

The answer depends on the context of which sides you are referring to, but typically if you provided two sides of a right triangle, they would often be the legs unless indicated otherwise.