The length of a rectangle is 3meters longer than the width. If the area is 34 square meters, find the rectangle's dimensions. Ro
1 answer:
You might be interested in
Answer:
x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.
Step-by-step explanation:
Let x be the length of wire that is cut to form a circle within the 5050 wire, so 5050 - x would be the length to form a square.
A circle with perimeter of x would have a radius of x/(2π), and its area would be
A square with perimeter of 5050 - x would have side length of (5050 - x)/4, and its area would be
The total combined area of the square and circles is
To find the maximum and minimum of this, we just take the 1st derivative, and set it to 0
Multiple both sides by 8π and we have
At x = 2221.5:
= 392720 + 500026 = 892746 [/tex]
At x = 0,
At x = 5050,
As 892746 < 1593906 < 2029424, x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.