Question

A triangle has sides with lengths of $6$ $\mathrm{feet}$, $8$ $\mathrm{feet}$, and $10$ $\mathrm{feet}$. Is it a right triangle?

Answer 1

Determine whether it is the right triangle or not.

According to the Pythagorean theorem, the square of the longest side of the triangle is equal to the sum of squares of the other two sides of the triangle.

Of the given lengths, $10$ $\mathrm{feet}$ is the longest. Determine the square of each length,

$\begin{array}{rcl}& \Rightarrow & 6^2=36\\ & \Rightarrow & 8^2=64\\ & \Rightarrow & {10}^2=100\end{array}$

Since $100=36+64$ or ${10}^2=6^2+8^2$, the given triangle follows the property of the right triangle.

Thus, the given lengths form a right triangle.