# Calculating perimeter with only area of a rectangle

• Jun 8th 2012, 04:57 AM
MikeNoob
Calculating perimeter with only area of a rectangle
I wanted to know how to calculate the perimeter of a rectangle if its area is 10.
I know that A=l x w
and Perimeter = 2l + 2W
How would i go about calculating the perimeter if its a Rectangle ?
• Jun 8th 2012, 05:00 AM
Prove It
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I wanted to know how to calculate the perimeter of a rectangle if its area is 10.
I know that A=l x w
and Perimeter = 2l + 2W
How would i go about calculating the perimeter if its a Rectangle ?

There are an infinite number of possibilities. Let \displaystyle \begin{align*} lw = 10 \implies w = \frac{10}{l} \end{align*}.

Then from the second equation we have

\displaystyle \begin{align*} P &= 2l + 2w \\ &= 2l + 2\left(\frac{10}{l}\right) \\ &= 2l + \frac{20}{l} \end{align*}

Obviously the perimeter will change if you change the value of w.
• Jun 8th 2012, 05:05 AM
Plato
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I wanted to know how to calculate the perimeter of a rectangle if its area is 10.
I know that A=l x w
and Perimeter = 2l + 2W
How would i go about calculating the perimeter if its a Rectangle ?

.
That is not possible.

A $1\times 10$ rectangle has perimeter $22$.

A $2\times 5$ rectangle has perimeter $12$.

Both have area $10$.
• Jun 8th 2012, 05:07 AM
MikeNoob
Re: Calculating perimeter with only area of a rectangle
I dont want to create another thread for this question what if a question states to find the length and width of a rectangle if its area is 48 and perimter is 28. The way i am doing it is that i am ending up with a quadratic equation. Any suggestion.
• Jun 8th 2012, 05:13 AM
Prove It
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I dont want to create another thread for this question what if a question states to find the length and width of a rectangle if its area is 48 and perimter is 28. The way i am doing it is that i am ending up with a quadratic equation. Any suggestion.

You can't solve a quadratic equation?
• Jun 8th 2012, 05:19 AM
MikeNoob
Re: Calculating perimeter with only area of a rectangle
I end up with the following equation:
l(square) + 48 -14l =0
When applying the quadratic formula i dont get the answer plus i get two values .. there must be an easier and a quicker way of solving this,
• Jun 8th 2012, 05:23 AM
Plato
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I end up with the following equation:
l(square) + 48 -14l =0
When applying the quadratic formula i dont get the answer plus i get two values .. there must be an easier and a quicker way of solving this,

You should have $l^2-14l+48=0$. That factors nicely.
• Jun 8th 2012, 05:51 AM
Prove It
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I end up with the following equation:
l(square) + 48 -14l =0
When applying the quadratic formula i dont get the answer plus i get two values .. there must be an easier and a quicker way of solving this,

Yes, you will get two values. What values did you get? If you use one of those values as the length, what do you get for the width?
• Jun 8th 2012, 07:02 AM
MikeNoob
Re: Calculating perimeter with only area of a rectangle
I get 8 and 6 ? how should i know which one to use ??
• Jun 8th 2012, 07:12 AM
Plato
Re: Calculating perimeter with only area of a rectangle
Quote:

Originally Posted by MikeNoob
I get 8 and 6 ? how should i know which one to use ??

One of those is length and the other is width. It does not matter which is which.