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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Properties of Triangles

NTA Abhyas 2020 · Mathematics · Properties of Triangles

Two medians drawn from acute angles vertices of a right angled...

Two medians drawn from acute angles vertices of a right angled triangle intersects at an angle π6\dfrac{π}{6}. If the length of the hypotenuse of the triangle is 33 units, then area of the triangle (in sq. units) isTwo medians drawn from acute angles vertices of a right angled triangle intersects at an angle (π)/(6) . If the length

Options

  1. A3\sqrt{3}
  2. B33
  3. C2\sqrt{2}
  4. D99

Correct answer

A. 3\sqrt{3}

Step-by-step solution

Slope of AG=−b2a,tan30o=3b2a1+b2a2AG = - \dfrac{b}{2a} , tan{30}^{o} = \dfrac{\dfrac{3b}{2a}}{1 + \dfrac{b^{2}}{a^{2}}}

Two medians drawn from acute angles vertices of a right angled triangle intersects at an angle (π)/(6) . If the length

a2+b2=9⇒13=3b.a2(a2+b2)a^{2} + b^{2} = 9 ⇒ \dfrac{1}{\sqrt{3}} = \dfrac{3b. a}{2\left(a^{2} + b^{2}\right)}

⇒12ab=(a2+b233)=933=3⇒ \dfrac{1}{2}ab = \left(\dfrac{a^{2} + b^{2}}{3\sqrt{3}}\right) = \dfrac{9}{3\sqrt{3}} = \sqrt{3}
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