Sides of 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

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(i) The sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of these sides, we will obtain 49, 576, and 625. 49 + 576 = 625 Or, Satisfies the pythagoras theorem It is a right triangle. The length of the hypotenuse is is 25 cm. (ii) The sides of the triangle are 3 cm, 8 cm, and 6...
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(i) The sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of these sides, we will obtain 49, 576, and 625. 49 + 576 = 625 Or, Satisfies the pythagoras theorem It is a right triangle. The length of the hypotenuse is is 25 cm. (ii) The sides of the triangle are 3 cm, 8 cm, and 6 cm. Squaring the lengths of these sides, we will obtain 9, 64, and 36. However, 9 + 36 ≠ 64 Or, 32+ 62≠ 82 The sum of the squares of the lengths of two sides is not equal to the square of the length of the third side. Therefore, the given triangle is not satisfying Pythagoras theorem. Hence, it is not a right triangle. (iii)The sides are 50 cm, 80 cm, and 100 cm. Squaring the lengths of these sides, we will obtain 2500, 6400, and 10000. However, 2500 + 6400 ≠ 10000 Or, 502+ 802≠ 1002 The sum of the squares of the lengths of two sides is not equal to the square of the length of the third side. Therefore, the given triangle is not satisfying Pythagoras theorem. Hence, it is not a right triangle. (iv)Thesides are 13 cm, 12 cm, and 5 cm. Squaring the lengths of these sides, we will obtain 169, 144, and 25. 144 +25 = 169 Or, The sides of the given triangle are satisfying Pythagoras theorem. Therefore, it is a right triangle. The length of the hypotenuse of this triangle is 13 cm. read less
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Tick the correct answer and justify :

In , AB = cm, AC = 12 cm and BC = 6 cm. The angle B is :

(A)  (B)  (C) (D)

Given : AB = 6√3cm AC= 12 cm BC=6 cm Ans : check if (AC)²=(BC)²+(AB)² 12²=(6)²+(6√3)² 144= 36+108 144=144 Angle B is 90º Option (C) is correct
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