Question

For any right triangle, the side lengths of the triangle can be put in the equation a^2+ b^2 = c^2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?

Answer 1

It is given that the side lengths of any right triangle can be put in the equation:

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

For a triangle with the side lengths 3 inches, 4 inches, and 5 inches, it can be substituted in two ways that will make the equation true:

Let a=3, b=4, and c=5:

`\begin{gathered} 3^2+4^2=5^2 \\ \Rightarrow9+16=25 \\ \Rightarrow25=25 \end{gathered}`

Hence, the equation is true.

You can also substitute a=4, b=3, and c=5.

This will also give the same result.

Notice that variable c has to match the longest side length.

The reason for this is that equality can only hold if the longest side is the variable at the right, if not there'll be an inequality instead.