In ⊥∆ABC, ∠B = 90°.
Let AB = a, BC = b,
Hypotenuse AC = c then
AC2 = AB2 + BC2
c2 = a2 + b2
∴ Here diagonal is the greatest side.
(i) a, b,c
7 cm, 24 cm, 25 cm,
c2 = a2 + b2
252 = (7)2 + (24)2
625 = 49 + 576
625 = 625
625 = 49 + 576
625 = 625
∴ This is right angled triangle.
Measurement of Hypotenuse, c = 25 cm.
ii) a c b
3 cm, 8 cm, 6 cm.
c2 = a2 + b2
82 = (3)2 + (6)2
64 = 9 + 36
64 ≠ 45
∴ These are not sides of right angled triangle.
iii) a b c
50 cm, 80 cm, 100 cm.
c2 = a2 + b2
1002= (50)2 + (80)2
10000 = 2500 + 6400
10000 ≠ 8900
∴ These are not sides of right angled triangle.
iv) a b c
12 cm, 5 cm, 13 cm,
c2 = a2 + b2
132 = (12)2 + (5)2
169 = 144 + 25
169 = 169
∴ These are sides of right angled triangle.
Measurement of Hypotenuse =13 cm.
