Question

If c is the hypotenuse of a right triangle, of sides a, b and c, find the third side. (i) b = 12 cm and c = 13 cm (ii) a = 8 cm and b = 6 cm (iii) a = 9 cm and c = 41 cm ​

Answer 1

Answer:

Step-by-step explanation:

If c is the hypotenuse of a right triangle, of sides a, b and c, then Pythagoras theorem is given as : a² + b² = c²

i) b = 12 cm and c = 13 cm

a² + b² = c²

⇒ a² + 12² = 13²

⇒ a² + 144 = 169

⇒ a² = 169 - 144 = 25

⇒ a = √25

⇒ a = 5cm

ii) a = 8cm, b = 6 cm

a² + b² = c²

⇒ 8² + 12² = c²

⇒ 64 + 36 = c²

⇒ c² = 100

⇒ c = √100

⇒ c = 10 cm

i) a = 9 cm and c = 41 cm

a² + b² = c²

⇒ 9² + b² = 41²

⇒ 81 + b² = 1681

⇒ b² = 1681- 81 = 1600

⇒ b = √1600

⇒ b = 40cm

Answer 2

Answer:

I) a=5cm

ii) c=10cm

iii) b=40cm