Table of Contents
- 1 What is the minimum amount of fence needed to completely enclose a rectangular area of 400 square meters?
- 2 What dimensions maximize the area of the pen?
- 3 What is the maximum area of a rectangle?
- 4 What is the minimum perimeter of a rectangle?
- 5 What dimensions should the farmer use to construct the pen with the largest possible area?
- 6 What point on the line is closest to the origin?
What is the minimum amount of fence needed to completely enclose a rectangular area of 400 square meters?
80 metres
What is the minimum amount of fence needed to completely enclose a rectangular area of 400 square metres? 80 metres. (To minimize the perimeter of a rectangle, make the rectangle into a square. The side lengths would all be 20m, so the perimeter would be 80m.)
What dimensions maximize the area of the pen?
Let the length of the pen be L and the width be W. One of the sides of the pen will be the barn. As we have to maximise the area of the pen that is constructed, the barn should form one of the longer sides of the pen. The required dimensions of the pen should be length 60 feet and width 30 feet.
What is the maximum area of a rectangle?
Approach: For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).
How do you maximize the area of a fence?
To maximize the area, each side perpendicular to the wall should have length x = 40 ft and the side parallel to the wall should have length y = 80 ft.
What is the largest rectangular area that can be enclosed by 800 yd fencing?
Hence if perimeter is 800 yards and it is a square, one side would be 8004=200 yards. Hence area can be maximized by fencing a square of side 200 yards.
What is the minimum perimeter of a rectangle?
16 in
Since there is no rule that states a rectangle cannot have all sides of equal length, all squares are rectangles, but not rectangles are squares. Hence, the minimum perimeter is 16 in with equal sides of 4 in.
What dimensions should the farmer use to construct the pen with the largest possible area?
With a given perimeter the rectangle with the greatest area is the square. The farmer should make 7 square pens. The pens need 22 sides. Each side is 400/22 feet, or 200/11 feet.
What point on the line is closest to the origin?
Closest point from origin will be the perpendicular distance from origin to the line. We need to find an equation of the perpendicular from (0,0) on y = 2x + 3.