Question

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

Answer 1

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=1/2xx6xx7sintheta=21sintheta`

For `Delta` to be maximum when `sintheta` is maximum .

So `theta=pi/2`

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