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Question: The perimeter of a rectangle is 104 m and it's area is 640 m^{2} . Find the length and breadth.




Perimeter (
p) = 104 m
Area (
a) = 640 m^{2}

Let the length be 
Let the breadth be b.

We know, 

So, one equation is 2(l+b)=104 m.

We also know that, l*b=a

Another equation is, l*b=640  m^{2} .

Let's work on the first equation - 2(l+b)=104 m.

=>  l+b= \frac{104}{2}  m

=>  l+b=52

∴ l=52-b

or, b=52-l

Now, it's time for the second equation - l*b=640  m^{2}

We already found on solving the upper equation that l is equal to 52-b.
And, b is equal to 52-l.

So, we can put any of the values in this equation and simplify to get the desired output (the values of breadth and length).

One way is, l*b=640  m^{2}

l is equal to 52-b.

=> (52-b)*b=640  m^{2}

=> 52-b= \frac{640}{b}   m^{2}

=> 52= \frac{640}{b}  m^{2}  + b

=> \frac{640}{b}  m^{2}  + b=52

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