Question:
In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
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Angles in A.P. in a triangle imply the middle angle is 60^∘.
Updated On: Mar 20, 2026
- \(5\pm\sqrt6\)
- \(3\sqrt3\)
- \(5\)
- None of these
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
If angles are in A.P., the middle angle is 60^∘.
Using cosine rule for sides 9 and 10 with included angle 60^∘:
a²=9²+10²-2(9)(10)\cos60^∘=81+100-90=91
a=3\sqrt3
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