Of all the rectangles with a perimeter of 100 feet, find the dimensions of the one with the largest area
1 answer:
You might be interested in
Answer:
44cm for minimum area and 0 for maximum area (circle)
Step-by-step explanation:
Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.
S + C = 100 or S = 100 - C
The side of square is S/4 and radius of the circle is
So the area of the square is
Therefore the total area is
We can substitute 100 - C for S
To find the maximum and minimum of this, we can take the first derivative and set that to 0
If we take the 2nd derivative:
We can see that this is positive, so our cut at 44 cm would yield the minimum area.
The maximum area would be where you not cut anything and use the total string length to use for either square or circle
if C = 100 then
if S = 100 then
So to yield maximum area, you should not cut at all and use the whole string to form a circle