How do I find the total area of three connected equally sized pens built so as to maximize the area bounded?
I'll be glad to help you,but there's no sides or measurement?
Sorry - the total amount of fencing is 240 feet
if the pens have equal width x, and length y, and are connected in a line, with the widths adjoining, then
6y + 4x = 240
x = (120-3y)/2
area a = 3xy
a = 3 (120-3y)/2 y
da/dy = 9(20-y)
a is max when y=20
so, x = 30
3xy = 1800 ft^2
To find the total area of three connected equally sized pens built to maximize the bounded area, there are a few steps you can follow:
1. Understand the setup: Visualize the three pens as identical rectangles, interconnected at their sides. Let's assume the length of each pen is L units and the width is W units.
2. Determine the arrangement: There are different ways you can arrange the pens to maximize the bounded area. One effective method is to position the pens in a linear arrangement, with two pens placed side by side and the third pen adjacent to them, creating an 'L' shape.
3. Calculate the area of each pen: The area of a rectangle is given by the formula A = length * width. For each pen, calculate its area by multiplying the length (L) by the width (W).
4. Find the total bounded area: To obtain the total bounded area, add up the areas of all three pens. Since the pens are identical, you can simply multiply the area of one pen by three: Total Area = 3 * Area of one pen.
By following these steps, you can efficiently calculate the total area of three connected equally sized pens constructed to optimize the bounded area.