I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.] ft (smaller value) ? ft (larger value)
ft2

Length =

Breadth =

Step-by-step explanation:

Let be the length of the garden

and be the width of the garden

From the details of the cost in the question we get

Now area of the garden is

Differentiating with respect to x we get

Equating with 0

Double derivative of the area is

So, area is maximum at

So, the length and breadth of the rectangle is .

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5