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

• A. \(5\pm\sqrt6\)
• B. \(3\sqrt3\)
• C. \(5\)
• D. None of these

Hint:

Angles in A.P. in a triangle imply the middle angle is 60^∘.

Answer 1

The Correct Option is B

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