Anonymous

How Do You Find The Dimensions Of A Rectangle If You Know The Perimeter And The Area?

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21 Answers

Anonymous Profile
Anonymous answered
IS THIS EQUATION IS DIMENSIONALLY CORRECT?
P= L + W   where P is the perimeter, L   is the length, and W is the width.
Anonymous Profile
Anonymous answered
Length of rectangle is 3 cm more than twice its width, area=35 cm2
Katie Harry Profile
Katie Harry answered
To find the area and perimeter of a rectangle you need to know formulas for each:
Area of a rectangle=L*W
Perimeter of a rectangle=2(L+W)
So to find either the area or the perimeter of a rectangle you need to know to things.
The value of:
The rectangles length
The rectangles width
To illustrate lets suppose that the length of the rectangle is 2 and the width is 3. Hence:
length= 2
width= 3
Area=2*3
Area=6
Perimeter=2(2+3)
Perimeter=2(5)
Perimeter=10
Anonymous Profile
Anonymous answered
Area=6cm2
perimeter=14cm

find the dimensions of the rectangle
Robin Lo Profile
Robin Lo answered
All rectangles of a given area will have the same perimeter,.Therefore knowing both will not help you to determine the dimensions.
thanked the writer.
Anonymous
Anonymous commented
This is a question in my neice's math homework. It is in the chapter about Quadradic & Exponential Functions.
janice boyd Profile
janice boyd answered
The length of a rectangle is 4 meters longer than it width.  If the perimeter of the rectangle is 60 meters, find the dimensions of the rectangle.
Anonymous Profile
Anonymous answered
The length of a rectangle is 6cm more than its width. If the area of the rectangle is 85cm^2, find the dimension
Anonymous Profile
Anonymous answered
The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width?
Anonymous Profile
Anonymous answered
A rectangle has sides that are 3x+1cm and 2x-5cm long. Its area is 39cm^2. What are the actual dimensions of the rectangle????
Anonymous Profile
Anonymous answered
The diagonal of frame is 5 inch. If the length of frame is 1 greater than it's width find the dimension of the frame?
Anonymous Profile
Anonymous answered
A rectangle has an area of 28cm2 and a perimeter of 22cm. What are the dimensions of the rectangle?

I dunt get this please help
David Hinners Profile
David Hinners answered
It is not true that all rectangles of a given area will have the same perimeter. To prove this to yourself, imagine a rectangle measuring 2 x 2, with a perimeter of 8, and area of 4. Then compare to a rectangle measuring 1 x 4, with a perimeter of 10, but with the same area of 4. To solve the problem of your question, you will need to do some algebra, as follows:
Perimeter = P = 2 (Length) + 2(Width) = 2L + 2W
Area = A = (Length)(Width) = LW
Rearrange the equation for perimeter to find W:
P = 2L + 2W = 2( L + W)
(P/2) = L + W
W = (P/2) - L
If you substitute this value into the Area equation,
A = LW = L( (P/2) - L) = (PL/2)-(L^2)
A = -L^2 + (PL/2)
Or, rearranging into standard form,
L^2 -(P/2)L+A=0
Now you can use the quadratic formula to solve for L.

Remember that for an equation in standard form,
aX^2 + bX + c = 0

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

So our equation (where x is L) has
a = 1
b = (P/2)
c = A

Which gives

L = (-(P/2) +/- sqrt((P/2)^2 - 4A)) / 2

Now, given perimeter and area, you can solve for the dimensions. As an example, P = 15, A = 14

L = (-(15/2) +/- sqrt((15/2)^2 - 4*14)) / 2

L = (-7.5 +/- .5) / 2 = -8 / 2 OR -7 / 2

L = 4 OR 3.5
(You can change the length to a positive number because when measuring length, positive or negative just depends on the direction)

You get 2 answers due to the way the quadratic formula works. However, it makes sense, because you would get two different answers depending on whether the Length or Width of your rectangle was the long dimension. So, choosing L=4, the dimensions of the recangle would be 4 x 3.5 .
As a check,
A = LW = (4)(3.5) = 14
p = 2L + 2W = 2(4) + 2(3.5) = 8 + 7 = 15
thanked the writer.
Anonymous
Anonymous commented
Thank you
even though i wasnt the one to ask the question
this answer really helped me because it explains everything step by step
ill make sure to ask you my algebra questions in the future!
Oddman Profile
Oddman answered
You can write a quadratic equation and solve it.
area = L*W
perimeter = 2(L+W)

area = L*(perimeter/2 - L) (substitute for W)
L2 - (perimeter/2)*L + area = 0 (rearrange to standard form)
L = (perimeter/2 ±√((perimeter/2)2 - 4(area)))/2 (use the quadratic formula)
L = perimeter/4 ± √(perimeter2/16 - area) (simplify)

Please note that there are two possible values for L. If you were to solve for W, you would get the same equation. This means that W is one of the values and L is the other. If you want L > W, then you will choose
L = perimeter/4 + √((perimeter/4)2 - area)
W = perimeter/4 - √((perimeter/4)2 - area)

Example
Suppose we know the perimeter of a 2x3 plot is 10, and its area is 6. Our formulas give
L = 10/4 + √((10/4)2-6) = 2.5 + √(6.25-6) = 2.5+.5 = 3
W = 2.5 - .5 = 2
_____
You will note that L = W = perimeter/4 = √area if the figure is a square.
Anonymous Profile
Anonymous answered
The length of a room, rectangular in shape, is 8 feet greater than its width. If the perimeter of the room is 64 feet, what are the dimensions of the room?
Anonymous Profile
Anonymous answered
The length of a rectangle is 5 cm less than 3 times its width. If the perimeter of the rectangle is 46 cm, find the dimensions of the rectangle.
Darren Joseph Profile
Darren Joseph answered
The perimeter of a rectangle is 170 inches. If the length is 5 more than three times the width what is the dimensions? Is this the formula 2L(5+3w)+2w=170 ?
diane nichols Profile
diane nichols answered
The perimeter of a rectangle is 80.  The length is 5 feet longer than 4 times the width.  What are the dimensions of the rectangle?  What is the area of the rectangle?

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