Question

the perimeter of a rectangle is 104m and its area is 640 m^2.find length and breadth.

Answer 1

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

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Answer:

Given,

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

Let the length be $l$.
Let the breadth be $b$.

We know, $2(l+b)=p$.

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 $52-b$.
So,

=> $(52-b)*b=640$  $m^{2}$

=> $52-b= \frac{640}{b}$  $m^{2}$

=> $52= \frac{640}{b}$ $m^{2}$ $+$ $b$

=> $\frac{640}{b}$ $m^{2}$ $+$ $b=52$