they have 25 feet of fencing to build the compost bin what is the area of the largest bin they can build? what are the dimensions of the bin with the largest area
A square will provide the largest area.
25/4 = ?
The largest bin (largest area) is obtained when you have a square, so each side is 25/4 ft
and the largest area is (25/4) ft^2
= 625/16 ft^2 or 39.0625 ft^2
To find the area of the largest compost bin that can be built with 25 feet of fencing, we need to consider the shape of the bin.
Let's assume the bin is in the shape of a rectangle. The perimeter of a rectangle is given by the formula P = 2w + 2l, where w is the width and l is the length of the rectangle. Given that the perimeter is 25 feet, we can write the equation as:
2w + 2l = 25
To find the dimensions that maximize the area of the rectangle, we can use the calculus concept of optimization. The area, A, of the rectangle is given by the formula A = w * l.
To find the dimensions that maximize the area, we can solve the equation by substitution.
First, we can solve the equation for w as a function of l:
2w + 2l = 25
2w = 25 - 2l
w = (25 - 2l) / 2
w = 12.5 - l
Now we substitute this expression for w in the area formula:
A = w * l = (12.5 - l) * l
To find the value of l that maximizes A, we take the derivative of A with respect to l and set it equal to zero:
dA/dl = 12.5 - 2l = 0
12.5 = 2l
l = 12.5 / 2
l = 6.25
Now we substitute this value of l back into the equation for w:
w = 12.5 - l
w = 12.5 - 6.25
w = 6.25
Therefore, the dimensions of the bin with the largest area are a width of 6.25 feet and a length of 6.25 feet.
To find the area, we can substitute these values into the area formula:
A = w * l
A = 6.25 * 6.25
A = 39.06 square feet
So, the area of the largest compost bin that can be built with 25 feet of fencing is approximately 39.06 square feet, and its dimensions are a width of 6.25 feet and a length of 6.25 feet.