I'll solve each right triangle problem using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse (the longest side opposite the right angle).
Let me work through each one carefully:
Triangle 1: Finding a
- Given: legs are 6cm and 8cm, need to find hypotenuse a
- a² = 6² + 8²
- a² = 36 + 64
- a² = 100
- a = √100 = 10 cm ✓
Triangle 2: Finding d
- Given: hypotenuse is 13cm, one leg is 12cm, need to find other leg d
- d² + 12² = 13²
- d² + 144 = 169
- d² = 169 - 144
- d² = 25
- d = √25 = 5 cm ✓
Triangle 3: Finding b
- Given: legs are 5cm and 12cm, need to find hypotenuse b
- b² = 5² + 12²
- b² = 25 + 144
- b² = 169
- b = √169 = 13 cm ✓
Triangle 4: Finding e
- Given: hypotenuse is 5cm, one leg is 3cm, need to find other leg e
- e² + 3² = 5²
- e² + 9 = 25
- e² = 25 - 9
- e² = 16
- e = √16 = 4 cm ✓
Triangle 5: Finding c
- Given: legs are 3cm and 4cm, need to find hypotenuse c
- c² = 3² + 4²
- c² = 9 + 16
- c² = 25
- c = √25 = 5 cm ✓
Triangle 6: Finding f
- Given: hypotenuse is 10cm, one leg is 8cm, need to find other leg f
- f² + 8² = 10²
- f² + 64 = 100
- f² = 100 - 64
- f² = 36
- f = √36 = 6 cm ✓
Final Answer:
a = 10 cm
d = 5 cm
b = 13 cm
e = 4 cm
c = 5 cm
f = 6 cm
Parent Tip: Review the logic above to help your child master the concept of copyright pythagorean theorem worksheet.
