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The problem can also be solved via Pythagoras theorem.

We know that: given two sides of a triangle, the area is maximized if we form a right-angled triangle using those two sides (since we want to maximize height * width)

Hence the third side - hypotenuse = sqrt( (11)squared + (5)squared ) = 12.083

I got a simple way. Please advise if it is not valid.

Let the triangle be ABC where AB=5 and AC=11.

The area of the triangle is given by

1/2 * (AB) * (AC) * sin(A)

= 1/2 * 5 * 11 * sin(A)

Because -1 <= sin(A) <= 1

In order to maximize it, we take sin(A) = 1

It means A = 90deg

Therefore,

BC = sqrt(5^2 + 11^2) (pyth. theorem)

BC = sqrt(146)

BC = 12.08

The area is given by 5 * 11 / 2 = 27.5

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