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How do you calculate the top dimensions of a rectangle if you know its perimeter and bottom area?
Important to note are these formulae:
Perimeter_of_rectangle = 2 x (length + width)
Area_of_rectangle = length x width
So if the perimeter and area are known, then:
2 x (length + width) = perimeter
=> length + width = perimeter / 2
=> length = perimeter / 2 - width
length x width = area
=> (perimeter / 2 - width) x width = area (substituting for length given above)
=> perimeter / 2 x width - width2 = area
=> width2 - perimeter / 2 x width + area = 0
which is a quadratic and can be solved either by factorization or by using the formula:
width = (perimeter / 2 +/- sqrt(perimeter2 / 4 - 4 x area)) / 2
= (perimeter +/- sqrt(perimeter2 - 16 x area)) / 4
This will provide two values for the width. However, each of these values is the length for the other, so the larger value is the length and the smaller value is the width.
Sometimes only 1 value will be found for the width above. In this case, the rectangle is actually a square which means that the length and width are both the same.
Examples:
1. perimeter = 6, area = 2
width2 - perimeter / 2 x width + area = 0
=> width2 - 6 / 2 x width + 2 = 0
=> width2 - 3 x width + 2 = 0
=> (width - 2) x (width - 1) = 0
=> width = 2 or 1.
So the length is 2 and the width is 1.
2. perimeter = 12, area = 9
width2 - perimeter / 2 x width + area = 0
=> width2 - 12 / 2 x width + 9 = 0
=> width2 - 6 x width + 9 = 0
=> (width - 3)2 = 0
=> width = 3
So the rectangle is a square with both length and width of 3.
What else can I help you with?
Where did perimeter come from and when?
Perimeter didn't 'come from' anywhere. The concept of 'how long is the bottom of the outside of this thing' has always existed. Perimeter is just the name for 'how long is the bottom of the outside of this thing'. As an example, the perimeter of any one of the pyramids has always been the same.About 1600, the English word 'perimeter' was first used to describe 'the distance around the outside of stuff'But, that distance was the same long before that!
What is the perimeter of 10 squares in a row?
To determine the perimeter of 10 squares in a row, we need to know the side length of each square. Let's say each square has a side length of "s" units. The perimeter of one square is 4s, so the total perimeter of 10 squares in a row would be 10 * 4s = 40s units.
How do you find the surface area of a triangular prism?
Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)ORSurface Area= 1/2(B x h)(2) + (s1+s2+s3)hORSurface Area= (B x h) + (s1+s2+s3)hB= Base.H= Height.s1, s2, s3= Basically the perimeter of the base.Remember: the base of a triangular prism is not always on the bottom.
What is the formula to find area of a shape?
Depends on what shape you're looking to find the area of.Area of a rectangle = Length x Width x Height(same for parallelogram)Area of a triangle = 1/2 Base x Height or S^2 times root four divided by threeCircumference of a circle = 22/7 (of 3.14) x the diameter of the circle. A Square or Rectangle: Multiply the length of the rectangle by the width of the rectangle or the opposite. A Triangle: Multiply the the Base length (from the bottom of triangle to the tip on top) by the Width of the triangle. Then, divide your results in half. A Circle: Multiply the radius by radius by 3.14 (pi) to find answer.
How do you calculate area of column?
Surface Area = (Circumference)(Height)* Volume = ∏r2 x Height *If you want to include the top and the bottom in the surface area of the column you have to add the area of the top and bottom. So, the Total Surface Area = [(Circumference)(Height)] + 4(∏)(Radius2)
What is the perimeter of rectangle 3mx6m on the bottom of a triangle?
The perimeter is the sum of all four sides, so you need to calculate 2 x length + 2 x height. The fact that the rectangle is at the bottom of a triangle is irrelevant - except that in specific diagrams, information may be provided that lets you calculate the length or the width of the triangle.
How do you find out the perimeter?
The perimeter of any 2D shape is the sum of all of the individual sides. For example: the perimeter of a rectangle is = length of rectangle (top) + length of rectangle (bottom) + height of rectangle (Left) + height of rectangle (Right)
How do you solve the problem Nu is disigning a rectangular sandbox The bottom is 16 square feet which dimensions requie the least amount of material for the sides of the sandbox?
Ok, an important part of this is that shapes can be categorized into multiple groups. It goes something like this in this case: Quadrilateral V Rectangle V Square When dealing with shapes, regular polygons always have less perimeter than irregular for the same area. Here, a square would have a perimeter of 16, with 4x4 dimensions; the next closest rectangle would have a perimeter of 20, with dimensions of 8x2; the last rectangle you could make would have a perimeter of 34, with dimensions of 16x1.
Is length of the rectangle and the perimeter are the same?
No. The length is the measurement of the distance from the bottom to the top of the rectangle, or from one side to the other side. The perimeter is the distance all the way around the rectangle.
What is the width of a the bottom of a rectangle cage if its perimeter is 57 inches and the length is 14.3 inches?
It is 14.2 inches
How can you compute perimeter of a rectangle in a class named rectangle in c plus plus?
struct rectangle { private: int top, bottom, left, right; public: int get_width()const{return(right-left);} int get_height()const{return(bottom-top);} int get_perimeter()const{return((get_width()+get_height())*2);} }
Can a circle be inscribed in a rectangle?
Yes! It can(: you draw the circle in the rectangle with its top and bottom touching the top and bottom sides of the rectangle
How do you find the perimeter of a cylinder?
Let h be the height of the cylinder and r the radius of the circular top/bottom. If you cut the cylinder down one side and roll it out, you have a rectangle. The length of the side is h and the width would be 2pi*r (the perimeter of a circle). Therefore, the perimeter of a cylinder is 2pi*r + 2h
Is the width the side or the bottom of a rectangle?
In a rectangle,the longest side(bottom) is always the length.The width is always the shorter one.
What is the name of the shape that is a rectangle on the bottom and a smaller rectangle on the top?
A rectangular frustum.
Describe the net of a cylinder?
there's a rectangle in the middle and then a circle at the top and the bottom of the rectangle
What are the bottom bracket dimensions for this bicycle frame?
The bottom bracket dimensions for this bicycle frame are the measurements of the part that connects the crankset to the frame.
