SOLUTION: 3. A wire 100 inches long is bent into a rectangle. If the width is x, 3. How is length represented? What is the function for area? 4. What must be the dimensions of the rectang

Question 568975: 3. A wire 100 inches long is bent into a rectangle. If the width is
x,
3. How is length represented? What is the function for area?
4. What must be the dimensions of the rectangle so that area is a
maximum?
5. What is the maximum area possible?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
3. A wire 100 inches long is bent into a rectangle. If the width is
x,
3. How is length represented? What is the function for area?
4. What must be the dimensions of the rectangle so that area is a
maximum?
5. What is the maximum area possible?
==========================================
The perimeter P = 2(l+x) = 100
So l+x = 50 -> l = 50-x
The area, A = l*x = x(50-x) = 50x - x^2
To maximize the area, set dA/dx = 0:
dA/dx = 50 - 2x = 0
This gives x = 25, which means the length is also 25, so the area is maximized when it is a square
The maximum area is 25*25 = 625 in^2
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