Area of triangle

Relevant wiki: Area of Triangles - Heron's Formula

By using Heron't formula,

$\large \displaystyle A = \sqrt{s (s-a)(s-b)(s-c)}$

Where $s$ is the semi perimeter of the Triangle, $a,b,c$ are the sides of the triangles.

$\large \displaystyle s = \frac{10+6+3}{2} = \frac{19}{2}.$

By substituting in Heron's Formula, We get

$\large \displaystyle A = \sqrt{\frac{19}{2} \left(\frac{19}{2} - 10 \right) \left(\frac{19}{2} - 6 \right) \left(\frac{19}{2} - 3\right)}\\ \large \displaystyle A = \sqrt{- \frac{19}{2} \times \frac{1}{2} \times \frac{7}{2} \times \frac{13}{2}}.$

The Area of the triangle leads to imaginary value.

So such Triangle formation is not Possible.

$\large \displaystyle \therefore \text{Answer } = \color{#69047E}{\boxed{666}}.$

A triangle can be formed only when the sum of any two sides is greater than the third side. Here $6 + 3 < 10$ . So, such a triangle does not exists due to which its answer cannot be found.

The sum of any two edges will need to be larger than the third.

Here, 10 > 3+6..

Hence, Triangle not possible..