a pentagon with a perimeter of 30 m is to be constructed by adjoining an equilateral triangle to a rectangle. find the dimension of the rectangle and triangle that will maximize the area of the pentagon.
the image given is a triangle on top of a rectangle with x beside both sides of the triangle and y beside one of the widths of the rectangle. I'm not sure if i should include the line between the two shapes with the triangle or the rectangle. and whether i should add the bottom of the rectangle to the triangle since it is the same size as the triangle sides.
would it be A(x,y)=(sqrt(3)/4)x^2 + y^2
3x+4y=10 then solve for y which is y=(10-3x)/4
then where do i go from there?