InterviewSolution
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InterviewSolution
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In a triangle, the lengths of the two larger sides are 10 and 9,respectively. If the angles are in A.P., then the length of the third sidecan be`5-sqrt(6)`(b) `3sqrt(3)`(c)`5`(d) `5+sqrt(6)` |
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Answer» Correct Answer - `5 + sqrt6 " or " 5 - sqrt6` Given that the angle of triangle are in A.P., Let `angleA = x - d, angle B = x, angle C = x + d` Now, `angle A + angle B + angle C = 180^(@)` `rArr x - d + x + x + d = 180^(@)` `rArr 3x =180^(@)` `rArr x = 60^(@)` `:. Angle B = 60^(@)` Using cosine formula `cos B = (a^(2) + c^(2) -B^(2))/(2AC)`, we get `cos 60^(@) = (100 + c^(2) - 81)/(2 xx 10 xx c)` `rArr (1)/(2) = (19 + c^(2))/(2 xx 10c)` `rArr c^(2) - 10 c + 19 = 0` `rArr c = (10 +- sqrt(100 - 76))/(2)` `rArr c = 5 +- sqrt6` Given that `a = 10 and b = 9` are the longer sides Therefore, `c = 5 + sqrt6 and 5 - sqrt6` both are possible |
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