you need to fence a rectangular play zone for children, to fit into a right-triangular plot with sides measuring 6m and 20m. what is the maximum area play zone?

Question

you need a fence in a rectangular play zone for children to fit into a right triangular plot with sides measuring 6m and 20m. what is the maximum area of this play zone?

Answer 1

Make a sketch showing the triangular area in the first quadrant with the hypotenuse running through the origin.

The equation of the hypotenuse is y = 10x/3 since it goes through the points (0,0) and (6,20)

 

The width of the rectangle = 6-x and the height = y = 10x/3

 

The area of the rectangle (6-x)*10x/3 = (1/3)*(60x-10x²) 

 

The derivative of area = 60 - 20x = 0 at the maximum point => x = 3

 

The w= 3 and h = 10