Let's solve each of these right triangle problems using the
Pythagorean Theorem, which states:
$$
a^2 + b^2 = c^2
$$
Where:
- $ a $ and $ b $ are the legs of the right triangle,
- $ c $ is the hypotenuse (the side opposite the right angle, and the longest side).
We'll identify which side is missing in each triangle and apply the formula accordingly.
---
1)
Triangle with legs: $ x $ and 4, hypotenuse: 5
$$
x^2 + 4^2 = 5^2 \\
x^2 + 16 = 25 \\
x^2 = 25 - 16 = 9 \\
x = \sqrt{9} = 3
$$
✔ Answer: $ x = 3 $
---
2)
Legs: 12 and 16, hypotenuse: $ x $
$$
12^2 + 16^2 = x^2 \\
144 + 256 = x^2 \\
x^2 = 400 \\
x = \sqrt{400} = 20
$$
✔ Answer: $ x = 20 $
---
3)
Leg: $ x $, leg: 16, hypotenuse: 20
$$
x^2 + 16^2 = 20^2 \\
x^2 + 256 = 400 \\
x^2 = 400 - 256 = 144 \\
x = \sqrt{144} = 12
$$
✔ Answer: $ x = 12 $
---
4)
Leg: 3, leg: $ x $, hypotenuse: 5
$$
3^2 + x^2 = 5^2 \\
9 + x^2 = 25 \\
x^2 = 25 - 9 = 16 \\
x = \sqrt{16} = 4
$$
✔ Answer: $ x = 4 $
---
5)
Leg: 12, leg: $ x $, hypotenuse: 20
$$
12^2 + x^2 = 20^2 \\
144 + x^2 = 400 \\
x^2 = 400 - 144 = 256 \\
x = \sqrt{256} = 16
$$
✔ Answer: $ x = 16 $
---
6)
Leg: 6, leg: $ x $, hypotenuse: 10
$$
6^2 + x^2 = 10^2 \\
36 + x^2 = 100 \\
x^2 = 100 - 36 = 64 \\
x = \sqrt{64} = 8
$$
✔ Answer: $ x = 8 $
---
✔ Final Answers:
1) $ x = 3 $
2) $ x = 20 $
3) $ x = 12 $
4) $ x = 4 $
5) $ x = 16 $
6) $ x = 8 $
All solved using the Pythagorean Theorem! Let me know if you'd like a visual explanation or step-by-step diagram.
Parent Tip: Review the logic above to help your child master the concept of pythagoras theorem problems worksheet.
