Stupid trapezoids

[Haphazard]

You know the trough optimization problems. I used to be able to do these easily and I completely forgot how to do them so I need help.

Trapezoids are 1/2h(a+b), in this case a is the long side, and we're trying to maximize area, which in this case will be y. We know that y and both sides of the trapezoids are 12", so by this we know that h^2=12^2 - .5(a-b)^2. However, if we plug this in and derive we end up with impenetrable square-root barf. I know that there's an easier way to do this. Help?

 

[Andy]

You know the trough optimization problems. I used to be able to do these easily and I completely forgot how to do them so I need help.

Trapezoids are 1/2h(a+b), in this case a is the long side, and we're trying to maximize area, which in this case will be y. We know that y and both sides of the trapezoids are 12", so by this we know that h^2=12^2 - .5(a-b)^2. However, if we plug this in and derive we end up with impenetrable square-root barf. I know that there's an easier way to do this. Help?

This doesn't seem to make any sense. Are you sure you are giving us the correct information? Your post states that you want to maximse the area y, but it also states 'that y and both sides of the trapezoids are 12"'. But if y=12" than it is fixed and cannot be optimised! Plus trapezoids usually gave 4 sides in everday existence, so by both sides do you mean a and h (or b and h). You can't mean a and b, otherwise thats a rectangle.

 

[Haphazard]

This doesn't seem to make any sense. Are you sure you are giving us the correct information? Your post states that you want to maximse the area y, but it also states 'that y and both sides of the trapezoids are 12"'. But if y=12" than it is fixed and cannot be optimised! Plus trapezoids usually gave 4 sides in everday existence, so by both sides do you mean a and h (or b and h). You can't mean a and b, otherwise thats a rectangle.

y is the area, 3 sides of the trapezoid are fixed at 12". The two sides referred to are the hypoteni of h, you know, the slanty ones, and there are two of them, because, you know, trapezoids have 4 sides.