Question

Observe the diagrams given below. Find the measures of the sides with question marks.

Answer 1

(1) By Pythagoras theorem,
(Hypotenuse)² = (side one)² + (side two)²

⇒ (20)² = (16)² + (side two)²
⇒ 400 = 256 + (side two)²
⇒ 400 − 256 = (side two)²
⇒ 144 = (side two)²
⇒ (12)² = (side two)²
Therefore, required side = 12 cm

(2) By Pythagoras theorem,
(Hypotenuse)² = (side one)² + (side two)²

⇒ (3.9)² = (side one)² + (1.5)²
⇒ 15.21 = (side one)² + 2.25
⇒ 15.21 − 2.25 = (side one)²
⇒ 12.96 = (side one)²
⇒ (3.6)² = (side one)²
Therefore, required side = 3.6 cm

(3) By Pythagoras theorem,
(Hypotenuse)² = (side one)² + (side two)²

⇒ (41)² = (40)² + (side one)²
⇒ 1681 = 1600 + (side two)²
⇒ 1681 − 1600 = (side two)²
⇒ 81 = (side two)²
⇒ (9)² = (side two)²
Therefore, required side = 9 cm