The sides of triangle are 6,7,x. Then the largest value of area of Delta is?

Jul 22, 2018

Let the angle opposite to the side $x$ be theta, then by cosine law of triangle we get

Now the area of the triangle

$\Delta = \frac{1}{2} \times 6 \times 7 \sin \theta = 21 \sin \theta$

For $\Delta$ to be maximum when $\sin \theta$ is maximum .

So $\theta = \frac{\pi}{2}$

And the largest area of the triangle wil be $21$