Absolutely! Let’s solve each of the 9 problems using the
Pythagorean Theorem:
>
Pythagorean Theorem: In a right-angled triangle,
>
a² + b² = c²
> where `a` and `b` are the lengths of the two legs (short sides), and `c` is the hypotenuse (longest side, opposite the right angle).
---
🔢 Problem 1:
Given: legs = 8 cm and 15 cm → find hypotenuse `c`
Solution:
a² + b² = c²
→ 8² + 15² = c²
→ 64 + 225 = c²
→ 289 = c²
→ c = √289 =
17 cm
✔ Answer: c = 17 cm
---
🔢 Problem 2:
Given: legs = 30 cm and 16 cm → find hypotenuse `c`
Solution:
30² + 16² = c²
→ 900 + 256 = c²
→ 1156 = c²
→ c = √1156 =
34 cm
✔ Answer: c = 34 cm
---
🔢 Problem 3:
Given: legs = 75 cm and 40 cm → find hypotenuse `c`
Solution:
75² + 40² = c²
→ 5625 + 1600 = c²
→ 7225 = c²
→ c = √7225 =
85 cm
✔ Answer: c = 85 cm
---
🔢 Problem 4:
Given: hypotenuse = 25 cm, one leg = 15 cm → find other leg `b`
Solution:
a² + b² = c² → rearrange to: b² = c² - a²
→ b² = 25² - 15²
→ b² = 625 - 225 = 400
→ b = √400 =
20 cm
✔ Answer: b = 20 cm
---
🔢 Problem 5:
Given: hypotenuse = 30 cm, one leg = 18 cm → find other leg `b`
Solution:
b² = c² - a² = 30² - 18²
→ b² = 900 - 324 = 576
→ b = √576 =
24 cm
✔ Answer: b = 24 cm
---
🔢 Problem 6:
Given: hypotenuse = 52 cm, one leg = 20 cm → find other leg `b`
Solution:
b² = 52² - 20²
→ b² = 2704 - 400 = 2304
→ b = √2304 =
48 cm
✔ Answer: b = 48 cm
---
🔢 Problem 7:
Given: hypotenuse = 60 cm, one leg = 48 cm → find other leg `a`
Solution:
a² = c² - b² = 60² - 48²
→ a² = 3600 - 2304 = 1296
→ a = √1296 =
36 cm
✔ Answer: a = 36 cm
---
🔢 Problem 8:
Given: hypotenuse = 35 cm, one leg = 28 cm → find other leg `a`
Solution:
a² = 35² - 28²
→ a² = 1225 - 784 = 441
→ a = √441 =
21 cm
✔ Answer: a = 21 cm
---
🔢 Problem 9:
Given: hypotenuse = 68 cm, one leg = 60 cm → find other leg `a`
Solution:
a² = 68² - 60²
→ a² = 4624 - 3600 = 1024
→ a = √1024 =
32 cm
✔ Answer: a = 32 cm
---
##
✔ Final Answers Summary:
| Problem | Answer |
|---------|------------|
| 1 |
17 cm |
| 2 |
34 cm |
| 3 |
85 cm |
| 4 |
20 cm |
| 5 |
24 cm |
| 6 |
48 cm |
| 7 |
36 cm |
| 8 |
21 cm |
| 9 |
32 cm |
---
💡
Tip: Always identify which side is the hypotenuse (the side opposite the right angle — it’s always the longest side). If you’re solving for a leg, subtract the square of the known leg from the square of the hypotenuse. If solving for the hypotenuse, add the squares of the two legs.
Let me know if you’d like to see diagrams or step-by-step visuals for any problem!
Parent Tip: Review the logic above to help your child master the concept of the pythagorean theorem worksheet.
