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In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:(i) 5, 7, 9(ii) 2, 10, 15(iii) 3, 4, 5(iv) 2, 5, 7(v) 5, 8, 20 |
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Answer» (i) Given 5, 7, 9 Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side. Here, 5 + 7 > 9, 5 + 9 > 7, 9 + 7 > 5 (ii) Given 2, 10, 15 No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case. (iii) Given 3, 4, 5 Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of triangle is always greater than the third side. Here, 3 + 4 > 5, 3 + 5 > 4, 4 + 5 > 3 (iv) Given 2, 5, 7 No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case. Here, 2 + 5 = 7 (v) Given 5, 8, 20 No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case. Here, 5 + 8 < 20 |
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