2 shorter sides of a right triangle have a length of 6 cm and 8 cm what is the parameter of the triangle

1 answer

To find the perimeter of the right triangle, we first need to determine the length of the hypotenuse. We can use the Pythagorean theorem, which states that \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the two shorter sides and \( c \) is the hypotenuse.

Given:
- \( a = 6 \, \text{cm} \)
- \( b = 8 \, \text{cm} \)

We need to find \( c \).

\[
6^2 + 8^2 = c^2
\]

\[
36 + 64 = c^2
\]

\[
100 = c^2
\]

\[
c = \sqrt{100}
\]

\[
c = 10 \, \text{cm}
\]

Now that we have the lengths of all three sides of the triangle, we can find the perimeter by adding them together:

\[
\text{Perimeter} = a + b + c
\]

\[
\text{Perimeter} = 6 + 8 + 10
\]

\[
\text{Perimeter} = 24 \, \text{cm}
\]

So, the perimeter of the triangle is 24 cm.