Question 1102530
.
the perimeter of a rectangular  garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % , 
we get the same perimeter. then the length and breadth of the new formed rectangular garden , respectively are
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        -----------------------------------------------------------------------------------------------
        The solution by @josgarithmetic is not correct.  The correct solution is placed below.
        -----------------------------------------------------------------------------------------------



<pre>
Let L be the length and W be the width of the rectangular garden (the original dimensions).


Then the first equation is

2L + 2W = 420,   or  L + W = 210.


The second equation is 

2*(1.2L) + 2*(0.6W) = 420,   or  1.2L + 0.6W = 210.


So, you have the system of 2 equations in 2 unknowns

   L +    W = 210,    (1)
1.2L + 0.6W = 210.    (2)


From eq(1) express W = 210-L  and substitute it into eq(2). You will get

1.2L + 0.6*(210-L) = 210,

1.2L + 0.6*210 - 0.6L = 210  ====>  0.6L = 210 - 0.6*210 = 0.4*210  ====>  L = {{{(0.4*210)/0.6}}} = 140.


Thus we just found L = 140 cm.


Then W = 210 - L = 210 - 140 = 70 cm.


The original length was 140 cm.  The original width was 70 cm.


<U>Check</U>.   140 + 70 + 140 + 70 = 420.    ! Correct !

         2*140*1.2 + 2*70*0.6 = 420.   ! Correct !


The new dimensions are:  1.2*L = 1.2*140 = 168 cm (length)  and  0.6*W = 0.6*70 = 42 cm.


<U>Answer</U>.  The new dimensions are:  168 cm (length)  and  42 cm (width).
</pre>

Solved.