Examples of Pythagorean Theorem problems

📚 Quick Study Guide

• 📐 The Pythagorean Theorem applies only to right triangles.
• 📝 It states: $a^2 + b^2 = c^2$, where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse.
• ➕ The hypotenuse is always the side opposite the right angle and is the longest side of the triangle.
• 💡 To find a missing leg length (a or b), rearrange the formula: $a = \sqrt{c^2 - b^2}$ or $b = \sqrt{c^2 - a^2}$.
• 🔢 Remember to take the square root after performing the subtraction to find the length of the side.

🧮 Practice Quiz

1. What is the length of the hypotenuse of a right triangle with legs of length 3 and 4?
1. 5
2. 7
3. 25
4. 12
2. A right triangle has a hypotenuse of length 13 and one leg of length 5. What is the length of the other leg?
1. 8
2. 12
3. 144
4. 18
3. A ladder is leaning against a wall. The base of the ladder is 6 feet from the wall, and the ladder reaches 8 feet up the wall. How long is the ladder?
1. 10 feet
2. 14 feet
3. 2 feet
4. 48 feet
4. What is the area of a right triangle with legs of length 7 and 24?
1. 84
2. 168
3. 31
4. 62
5. Find the value of $x$ in the right triangle where one leg is 9, the other leg is 12 and the hypotenuse is $x$.
1. 15
2. 3
3. 21
4. 225
6. If $a = 6$ and $c = 10$, find the length of side $b$ in the right triangle.
1. 8
2. 4
3. 16
4. 100
7. A square has sides of length 5. What is the length of the diagonal of the square?
1. $\sqrt{50}$
2. 5
3. 10
4. 25