Question

Determine if the side lengths form a right triangle. If not, is the longest side too long or too short ? 9,40,41

Answer 1

We know that a right triangle satisfies the pythagorean theorem:

`c^2=a^2+b^2`

where a and b are the legs (the two smaller sides) and c is the hypotenuse.

To determine if the sides form a right triangle we plug the values into the pythagorean theorem, if the equation holds then the sides form a right triangle:

`\begin{gathered} 41^2=40^2+9^2 \\ 1681=1600+81 \\ 1681=1681 \end{gathered}`

Since the equation holds we conclude that the sides given form a right triangle.