CBSE Questions for Class 9 Maths Heron'S Formula Quiz 6 - MCQExams.com

Considering $$\left| \overline { a }  \right| =14$$,  $$\left| \overline { b }  \right| =18$$,  So, $$\left| \overline { a } -\overline { b }  \right| =16$$ and $$Q=\overline { a } \wedge \overline { b } $$

So, $$\left| \overline { a } -\overline { b }  \right| =16=\sqrt { { \left| \overline { a }  \right|  }^{ 2 }+{ \left| \overline { b }  \right|  }^{ 2 }-2\left| \overline { a }  \right| \left| \overline { b }  \right| \cos\theta  } $$

      $$256=196+324-2\left( 14 \right) \left( 18 \right) \cos\theta $$

So  $$\cos\theta =0.523$$

other diagonal will be

$$\left| \overline { a } +\overline { b }  \right| =\sqrt { { \left| \overline { a }  \right|  }^{ 2 }+{ \left| \overline { b }  \right|  }^{ 2 }+2\left| \overline { a }  \right| \left| \overline { b }  \right| \cos\theta  } $$

$$\left| \overline { a } +\overline { b }  \right| =\sqrt { { 14 }^{ 2 }+{ 18 }^{ 2 }+2\left( 14 \right) \left( 18 \right) \left( 0.523 \right)  } $$

So, $$\left| \overline { a } +\overline { b }  \right| =$$ other diagonal $$=27.99\approx 28cm$$