Sides of some triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse (i) 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

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.

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