Re: Maxima Minima question

Hey numpty.

Hint: We know that a triangles area can be written in terms of A = 0.5*b*h. Can you use Pythagoras' Theorem to get h in terms of the other sides of the triangle (besides the base that is)?

Re: Maxima Minima question

you may have to walk me through this as i am still struggling

Re: Maxima Minima question

Given the three lengths, one is the base (b) and the height (h) is related to the two other sides.

The area of a triangle with lengths a and b and angle x in the middle is:

A = 1/2*a*b*sin(x) which you need to maximize.

You have a + b + c = 30 (the three sides) and you can get the angle using cos(x) = [b^2 + a^2 - c^2]/[2ab]

Now you have to eliminate the variables to get a maximum for A with respect to another variable (i.e. a,b, or c) using normal calculus.

Re: Maxima Minima question

Please check put if you have missed any part of the question that is some information about the type of triangle, isosceles / eqilateral.

Re: Maxima Minima question

I think it might be easier to use Heron's formula for the area of a triangle:

Fixing a and viewing b as a variable gives

Differentiating with respect to b gives , and since the first factor can not possibly be zero, , so . Therefore the triangle in question is isosceles.

Setting and viewing a as a variable gives , and differentiating gives , so and the triangle is equilateral.

I don't think the result is particularly surprising, but it's nice to see a proof.

- Hollywood