I'll work through each problem step by step using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse (longest side).
Problem 1: Given sides 17 and 19, find missing side
- The longest given side is 19, so it could be the hypotenuse
- Let's check: if 19 is hypotenuse: 17² + ?² = 19²
- 289 + ?² = 361
- ?² = 72
- ? = √72 ≈ 8.5
Problem 2: Given sides 5 and 13, find missing side
- 13 is the longest, so it's the hypotenuse
- 5² + ?² = 13²
- 25 + ?² = 169
- ?² = 144
- ? = 12
Problem 3: Given sides 10 and 20, find missing side
- 20 is the longest, so it's the hypotenuse
- ?² + 10² = 20²
- ?² + 100 = 400
- ?² = 300
- ? = √300 ≈ 17.3
Problem 4: Given sides 5 and 14, find missing side
- 14 is the longest, so it's the hypotenuse
- 5² + ?² = 14²
- 25 + ?² = 196
- ?² = 171
- ? = √171 ≈ 13.1
Problems 5-9: Already solved correctly on the worksheet!
Let me verify the answers shown:
- #5: a=12, b=5, c=13 ✓ (144+25=169)
- #6: a=8, b=6, c=10 ✓ (64+36=100)
- #7: a=15, b=8, c=17 ✓ (225+64=289)
- #8: a=30, b=40, c=50 ✓ (900+1600=2500)
- #9: a=2√3, b=2, c=4 ✓ (12+4=16)
Final Answer:
1. Missing side ≈ 8.5
2. Missing side = 12
3. Missing side ≈ 17.3
4. Missing side ≈ 13.1
5. c = 13
6. b = 6
7. b = 8
8. a = 30
9. a = 2√3
Parent Tip: Review the logic above to help your child master the concept of the pythagorean theorem worksheet answer key.
