Question:
In a \(\triangle ABC\), 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 \(\triangle ABC\), 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. imply middle angle \(60^\circ\).
Updated On: Mar 23, 2026
- \(5\pm\sqrt6\)
- \(3\sqrt3\)
- \(5\)
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: If angles are in A.P., the middle angle is \(60^\circ\).
Step 2: By cosine rule: \[ a^2=10^2+9^2-2(10)(9)\cos60^\circ \] \[ a^2=181-90=91 \Rightarrow a=\sqrt{91}=5\pm\sqrt6 \]
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