1. Sides of triangles are given below. Determine which of them are right thang
In case of a right triangle, write the length of its hypotenuse.
(1) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
D
Answers
Answer:
In a right angle
(hypotenuse)2 = (base)2 + (perpendicular)2 (from Pythagoras theorem)
square of largest number should be equal to the Sum of square other two numbers.
1. 7 cm, 24 cm, 25 cm
(25)2 = (24)2 + (7)2
=> 625 = 576 + 49
=> 625 = 625
So it forms a right triangle.
2. 3 cm, 8 cm, 6 cm
(8)2 = (6)2 + 32
=> 64 = 36 + 9
=> 64 = 45 (it is not possible)
So it does not form a right triangle.
3. 50 cm, 80 cm, 100 cm
(100)2 = (80)2 + (50 )2
=> 10000 = 6400 + 2500
=> 10000 = 8900 (it is not possible)
So it does not form a right triangle.
4. 13 cm, 12 cm, 5 cm
(13)2 = (12)2 + (5
)2
=> 169 = 144 + 25
=> 169 = 169
So it forms a right triangle.
Answer:
Answer
(i)
Since, (25)
2
=(7)
2
+(24)
2
⇒625=49+576⇒625=625
Hence, 7cm, 24cm and 25cm are the sides of Right Angled Triangle and its Hypotenuse is 25cm
(ii)
Since, (8)
2
=(3)
2
+(6)
2
⇒64
=45
Hence, 8cm, 6cm and 3cm do not form Right Angled Triangle.
(iii)
Since, (100)
2
=(50)
2
+(80)
2
⇒10000
=8900
Hence, 100cm, 50cm and 80cm do not form Right Angled Triangle.
(iv)
Since, (13)
2
=(12)
2
+(5)
2
⇒169=144+25⇒169=169
Hence, 13cm, 12cm and 5cm are the sides of Right Angled Triangle and its Hypotenuse is 13cm.