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AP EAMCET · Maths · Properties of Triangles

If 7 and 8 are the lengths of two sides of a triangle and ' \(a\) ' is the length of its smallest side. The angles of the triangle are in AP and ' \(a\) ' has two values \(a_1\) and \(a_2\) satisfying this condition. If \(a_1 \lt a_2\) then \(2 a_1+3 a_2=\)

  1. A 15
  2. B 21
  3. C 24
  4. D 28
Verified Solution

Answer & Solution

Correct Answer

(B) 21

Step-by-step Solution

Detailed explanation

Let angles be \(A, 180^{\circ}-3 A, 2 A\) Then \(2\left(180^{\circ}-3 A\right)=A+2 A \Rightarrow A=40\) \(\therefore\) Angles are \(40^{\circ}, 60^{\circ}, 80^{\circ}\) Now, \(b^2=c^2+a^2-2 a c \cos 60^{\circ} \Rightarrow 49=64+a^2-8 a\)…