Question

The lengths of the sides of some triangles
are given below. Find out which of them are
right- angled triangle.
(1) 4.5 cm, 6 cm, 7.5 cm
(2) 9 cm, 10 cm, 11 cm
(3) 10 cm, 20 cm, 30 cm
(4) 3.5 cm, 12 cm, 12.5 cm
(5) 12 cm, 16 cm, 20 cm
(6) 7.5 cm, 10 cm, 12.5 cm
(7) 6 cm, 12 cm, 13 cm
(8) 3 cm, 4 cm, 6 cm
(9) 1.5 cm, 3.6 cm, 3.9 cm​

Answer 1

Answer:

3, 5 and 9

Step-by-step explanation:

Answer 2

Step-by-step explanation:

(1) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (45)2 = (27)2 + (side two)2

⇒ 2025 = 729 + (side two)2

⇒ 2025 − 729 = (side two)2

⇒ 1296 = (side two)2

⇒ (36)2 = (side two)2

Therefore, second adjacent side = 36

(2) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (50)2 = (side one)2 + (side two)2

⇒ 2500 = (side one)2 + 196

⇒ 2500 − 196 = (side one)2

⇒ 2304 = (side one)2

⇒ (48)2 = (side one)2

Therefore, first adjacent side = 48

(3) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (6.1)2 = (6.0)2 + (side two)2

⇒ 37.21 = 36.0 + (side two)2

⇒ 37.21 − 36.0 = (side two)2

⇒ 1.21 = (side two)2

⇒ (1.1)2 = (side two)2

Therefore, second adjacent side = 1.1

(4) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (3.7)2 = (side one)2 + (3.5)2

⇒ 13.69 = (side one)2 + 12.25

⇒ 13.69 − 12.25 = (side one)2

⇒ 1.44 = (side one)2

⇒ (1.2)2 = (side one)2

Therefore, first adjacent side = 1.2

(5) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (25)2 = (7)2 + (side two)2

⇒ 625 = 49 + (side two)2

⇒ 625 − 49 = (side two)2

⇒ 576 = (side two)2

⇒ (24)2 = (side two)2

Therefore, second adjacent side = 24

(6) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (12.5)2 = (side one)2 + (10)2

⇒ 156.25 = (side one)2 + 100

⇒ 156.25 − 100 = (side one)2

⇒ 56.25 = (side one)2

⇒ (7.5)2 = (side one)2

Therefore, first adjacent side = 7.5

(7) By Pythagoras theorem,

(Hypotenuse)2 = (side one)2 + (side two)2

⇒ (7.5)2 = (6)2 + (side two)2

⇒ 56.25 = 36 + (side two)2

⇒ 56.25 − 36 = (side two)2

⇒ 20.25 = (side two)2

⇒ (4.5)2 = (side two)2

Therefore, second adjacent side = 4.5