Answer:
The answer is below
Step-by-step explanation:
Let us assume that the length of the square be x. Therefore the area of the square is given as:
Area of square = length × length = x × x = x²
Given that the length of one side of the rectangle is twice the length of the other side. Let the length of the small side be a therefore the length of the long side = 2a
The area of the rectangle = length of small side × length of long side = a × 2a = 2a²
Since both the rectangle and square are to occupy the same space, hence:
[tex]Area\ of\ rectangle=Area\ of \ square\\\\2a^2=x^2\\\\a=\sqrt{\frac{x^2}{2} }\\ \\a=\frac{x}{\sqrt{2} }[/tex]
Length of small side = a = [tex]\frac{x}{\sqrt{2} }[/tex], length of long side = 2a = [tex]\frac{2x}{\sqrt{2} }[/tex]
The length of the sides are length of the square side divide by √2 ([tex]\frac{x}{\sqrt{2} }[/tex]) and twice the length of the square side divide by √2 ([tex]\frac{2x}{\sqrt{2} }[/tex])
