A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are use
d, what is the maximum area that can be enclosed?
1 answer:
Answer:
Step-by-step explanation:
For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.
And we are interested about the maximum area.
For this case since we have a recatangular area we know that the area is given by:
Where L is the length and W the width, if we replace from the values on the figure we got:
And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.
If we find the first derivate respect to x we got:
We set this equal to 0 in order to find the critical points and for this case we got:
And if we solve for x we got:
We can calculate the second derivate for A(x) and we got:
And since the second derivate is negative then the value for x would represent a maximum.
Then since we have the value for x we can solve for the other side like this:
And then since we have the two values we can find the maximum area like this:
You might be interested in
A. You would start off by a rectangle in the middle, then you would place to squares on the bottom and top if the rectangle. After you've done that, you place two rectangles (Same size as the original) on both sides of the original rectangle. Finally you add a rectangle (Same size) to either ends of the secondary rectangles. It should look like this.
B. You would start off with a rectangle in the middle, then you would add 2 equilateral triangles to the top and bottom of the rectangle. After that, you Simply put 2 rectangles (Same size as the original) on both sides of the rectangle. It should look something like this.
C. To make a pyramid, it's actually quite simple. You would start off with a square in the middle, and then place equilateral triangles on ALL sides of the square. It should look something like this.
I hope this helped ^^
B. You would start off with a rectangle in the middle, then you would add 2 equilateral triangles to the top and bottom of the rectangle. After that, you Simply put 2 rectangles (Same size as the original) on both sides of the rectangle. It should look something like this.
C. To make a pyramid, it's actually quite simple. You would start off with a square in the middle, and then place equilateral triangles on ALL sides of the square. It should look something like this.
I hope this helped ^^