Solution :
(i) 7 cm, 24 cm, 25 cm
Let AB = 7 cm, BC = 24 cm, CA = 25 cm
then \({AB}^2\) = 49, \({BC}^2\) = 576 and \({CA}^2\) = 625
\({AB}^2\) + \({BC}^2\) = 625 = \({CA}^2\)
Yes, ABC is a right triangle and its hypotenuse is 25 cm.
(ii) 3 cm, 8 cm, 6 cm
Let AB = 3 cm, BC = 8 cm, CA = 6 cm
then \({AB}^2\) = 9, \({BC}^2\) = 64 and \({CA}^2\) = 36
\({AB}^2\) + \({CA}^2\) = 45 \(\ne\) \({BC}^2\)
No, ABC is not a right triangle.
(iii) 50 cm, 80 cm, 100 cm
Let AB = 50 cm, BC = 80 cm, CA = 100 cm
then \({AB}^2\) = 2500, \({BC}^2\) = 6400 and \({CA}^2\) = 10000
\({AB}^2\) + \({BC}^2\) = 8900 \(\ne\) \({CA}^2\)
No, ABC is not a right triangle.
(iv) 13 cm, 12 cm, 5 cm
Let AB = 13 cm, BC = 12 cm, CA = 5 cm
then \({AB}^2\) = 169, \({BC}^2\) = 144 and \({CA}^2\) = 25
\({BC}^2\) + \({CA}^2\) = 169 = \({AB}^2\)
Yes, ABC is a right triangle and its hypotenuse is 13 cm.
