Kira has feet of fencing. She will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. For the area of the garden to be the maximum, how long should the side opposite the house be?

Question

Kira has feet of fencing. She will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. For the area of the garden to be the maximum, how long should the side opposite the house be?

Answer 1

You failed to indicate how many feet of fencing Kira has.

Answer 2

let the perimeter be P, where P is a constant

let the length be y and the width be x
2x + y = P
y = P - 2x

Area = xy
= x(P-2x) - Px - 2x^2

d(area)/dx = P - 4x
= 0 for a maximum area
4x = P
x = P/4
y = P - P/2 = P/2

So the long side should be half the perimeter, and the short side whould be a quarter of the perimeter.

Answer 3

i need help with my math homework

Answer 4

if the perimeter of a rectangle is 184cm and the width is 39cm calculate its length

Answer 5

To find the length of the side opposite the house that will maximize the area of the garden, we can use the concept of optimization.

Let's assume the length of the side opposite the house is x feet. Since there are three sides that need fencing, the total length of these three sides is 3x.

Since Kira has a total of feet of fencing available, we can set up the equation:

3x =

This equation represents that the sum of the three sides of the rectangular garden is equal to the available fencing.

To maximize the area of the garden, we need to express the area of the garden in terms of x. The area of a rectangle is given by the formula:

A = length × width

Since the length is x, and the width is the side of the garden opposite the house, which we need to find, let's call it y.

So, the area of the garden is:
A = x × y

Now, the goal is to maximize this area (A). To find the optimal value of y, we differentiate the area function with respect to y:

dA/dy = x

Next, we need to solve for y when dA/dy = 0 to find the maximum value of the area. However, since we are not given any specific value for the available fencing (the value of x), we cannot determine the exact value of y.

Therefore, the length of the side opposite the house should be determined based on the specific value of the available fencing (x) provided in the question.