Pythagorean Theorem
Instructions
- The first videos below explain the concepts in this section.
- This page includes exercises that you should attempt to solve yourself and then check your answers.
- When you are done, you can use the graph to pick another section or use the buttons to go to the next section.
Learning Objectives
- The Pythagorean Theorem for right triangles
- Use the Pythagorean Theorem to determine a missing side length of a right triangle
Concept Video(s)
Exercises
1.
Answer: \(x=\sqrt{117}\)
Solution Method: Using the Pythagorean Theorem:
\begin{align*}
9^2+6^2 &= x^2 \\
81 + 36 &= x^2 \\
117 &= x^2 \\
\sqrt{117} &= x
\end{align*}
Solution Method: Using the Pythagorean Theorem:
\begin{align*}
9^2+6^2 &= x^2 \\
81 + 36 &= x^2 \\
117 &= x^2 \\
\sqrt{117} &= x
\end{align*}
2.
Answer: 5
Solution Method: Let \(a=\sqrt{5}\) be the length of the shorter leg. Then the longer leg, \(b\) is \(2a\), or \(b=2\sqrt{5}\). Then we can solve for the hypotenuse, \(c\), using the Pythagorean Theorem.
\begin{align*}
a^2+b^2 &= c^2 \\
(\sqrt{5})^2 + (2\sqrt{5})^2 &= c^2 \\
5 + (2^2) 5 &= c^2 \\
5+ (4)5 &= c^2 \\
5+20 &= c^2 \\
25 &= c^2 \\
\sqrt{25} &= \sqrt{c^2} \\
5&=c
\end{align*}
Solution Method: Let \(a=\sqrt{5}\) be the length of the shorter leg. Then the longer leg, \(b\) is \(2a\), or \(b=2\sqrt{5}\). Then we can solve for the hypotenuse, \(c\), using the Pythagorean Theorem.
\begin{align*}
a^2+b^2 &= c^2 \\
(\sqrt{5})^2 + (2\sqrt{5})^2 &= c^2 \\
5 + (2^2) 5 &= c^2 \\
5+ (4)5 &= c^2 \\
5+20 &= c^2 \\
25 &= c^2 \\
\sqrt{25} &= \sqrt{c^2} \\
5&=c
\end{align*}