Question

A triangle has sides of length $6,8,$ and $10$.

Is it a right triangle? Explain.

Answer 1

Identify the type of triangle:

The sides of the triangle are of lengths $6,8,$ and $10$.

The longest side length is $10$.

And the smaller sides are of lengths $6,8$.

Now, the sum of squares of the smaller sides is given as:

$\begin{array}{rcl}{6}^2+8^2& =& 36+64\\ & =& 100\end{array}$

And the square of the longer side is ${10}^2=100$.

As the sum of squares of the smaller sides is equal to the square of the longer side that is $6^2+8^2={10}^2$.

So, by the Pythagorean Theorem, the sides form a right triangle.

So, the triangle has sides of length $6,8,$ and $10$ is a right triangle.

Hence, the correct answer is yes and the given triangle is right triangle.