Lets consider the side of square be 'x' units
So as per data,
Length of rectangle is x+5
Breadth of rectangle is x/2
and also as per data, the areas of rectangle and square are equal.
Area of rectangle = Length * Breadth = (x+5)*x/2 = ( x^{2} +5x)/2 <- equation1
Area of square = Side* Side= x*x = x^{2} <- equation2
As per given data, Equation1 and equation 2 are equal
so
( x^{2} +5x)/2 = tex] x^{2} [/tex]
x^{2} +5x = 2 x^{2}
2 x^{2} - x^{2} = 5x
x^{2} = 5x
x = 5
So the side of square = 5 units
For Square, both dimensions are equal
