Question

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?

Answer 1

In a right-angled triangle, we can use the Pythagorean theorem to find the lengths of the sides. The theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\):

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

Given:
- Hypotenuse \(c = 10\) cm
- One side \(a = 6\) cm

We need to find the length of the other side \(b\). According to the Pythagorean theorem, we can rearrange the formula to solve for \(b\):

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

Substituting the known values:

\[
b^2 = 10^2 - 6^2
\]
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]

Now, taking the square root of both sides to find \(b\):

\[
b = \sqrt{64} = 8
\]

Thus, the length of the third side is \(8\) cm.