Question

Area of a rectangle becomes double when the length is twice the breadth and area of the rectangle becomes half when length is reduced 4 times the breadth. then find the dimensions of the rectangle...........................?
guys please say me the solution soon.................................................

Answer 1

Let A be area of rectangle with Length L and breadth B.
A = L B

2 A = 2B * B      =>   A = B²    or   B * B    ---- equation 1
                               As A = L B  => L = B    - equation 2

Area becomes half when Length is reduced 4 times breadth: means L is divided by 4B

A / 2  =   (L/4B) B  =>    A = L/2   -  equation 3

           A  = L / 2 = B²  = L B = L²

    B = 1/2   L = B = 1/2 
      
dimensions of rectangle are  :  L = 1/2    B =  1/2    Area = 1/4

Answer 2

Let area of rectangle be A
Length = x and breadth = y.
A = xy

Area becomes double when the length is twice the breadth
$2A = 2y*y = 2y^2$
$A = y^2$    .......(1)
 
Since A = xy 
⇒ x = y .......(2)

Area becomes half when Length is reduced 4 times breadth

$\frac{A}{2} = \frac{x}{4y}*y$

$A = \frac{x}{2}$    ......(3)

From equations
$A = \frac{x}{2} = xy$

$y = \frac{1}{2}$

Since, x = y therefore, $x = \frac{1}{2}$

So the dimensions are length = breadth = $\frac{1}{2}$

That means, the given figure is a square.