What is the answer to number 4 ?
2 answers:
You might be interested in
Answer:
Therefore the dimension of the rectangular piece of land is 375 m by 250 m.
Step-by-step explanation:
Given that,
Two opposite sides of rectangular land will be fenced using standard fencing that costs $6 per m while the other two side will require heavy duty fencing that costs $9 per m.
Let the length and width of the rectangular x and y respectively.
Then total cost for fencing =
=$(12x+18y)
Then,
12x+18y= 9,000
⇒ 2x+3y=1,500 [ cancel out common factor 6]
⇒3y= 1500 - 2x
....(1)
The area of the rectangular land is = Length × width
= xy
Let,
A=xy
Putting the value of y
Differentiating with respect to x
Again differentiating with respect to x
Now we have to determine the critical value of A.
For critical value set A'=0
⇒1500-4x=0
m
Since, . at x=375 m the area of the rectangular piece of land is maximum.
From equation (1) we get when x=375
⇒y=250 m
Therefore the dimension of the rectangular piece of land is 375 m by 250 m.