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Which of the following can be the sides of a right triangle ?In the case of right-angled triangles, identify the right angles.(i) 2.5 cm, 6.5 cm, 6 cm(ii) 2 cm, 2 cm, 5 cm(iii) 1.5 cm, 2 cm, 2.5 cms |
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Answer» (i) The greatest side is hypotenuse = 6.5 cm (2.5)2 + (6)2 = (6.5)2 (According to pythagoras property) 6.25 + 36 = 42.25 42.25 = 42.25 ∴ This is a right angled triangle. The given length can be the sides of a right angled triangle. The right angle between the lengths of 2.5 cm and 6 cm. (ii) The greatest side is 5 cm (2)2 + (2)2 = (5)2 (According to pythagoras property) 4 + 4 ≠ 25 ∴ It is not the lengths of right angled triangle. (iii) The greatest side is 2.5 cms. According to pythagoras property (2.5)2 = (1.5)2 + (2)2 6.25 = 2.25 + 4 6.25 = 6.25 It is a right angled trianges, the given lengths are sides of the right angled triangles. ∴ The right angle between the lengths of 1.5 cms and 2 cms. |
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