Question

Solve for the missing side of each right triangle. if the solution is not an integer express it in simplest radical form

Answer 1

2√(13)

Step-by-step explanation:

The Pythagorean theorem says that the longest side of a right triangle is equal to:

`c=\sqrt[]{a^2+b^2}`

Where a and b are the length of the other sides.

So, replacing a by 6 and b by 4, we get that the largest side of the triangle is equal to:

`\begin{gathered} c=\sqrt[]{6^2+4^2} \\ c=\sqrt[]{36+16} \\ c=\sqrt[]{52} \end{gathered}`

Finally, simplifying the radical, we get:

`\begin{gathered} c=\sqrt[]{52} \\ c=\sqrt[]{4(13)} \\ c=\sqrt[]{4}\text{ }\sqrt[]{13} \\ c=2\text{ }\sqrt[]{13} \end{gathered}`

Therefore, the length of the missing side is 2√(13)