The area of rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3rd of the side of the square. What is the side of the square ?

The correct answer is: ∴ Side of the given square is 15 cm.

Step-by-step solution:-
Let the Area of the given square be x² cm²
∴ Area of square = x² …............................................... (Equation i)
∴                         side2 = x² ….............................................. (Area of a square = side2)
∴                         side = x ................................... (Taking square root both the sides) ................................. (Equation ii)
Now, for the given rectangle-
∴ Breadth = 2/3 × side of square ...................................... (From given information)
∴ Breadth = 2/3 × x ................................... (From Equation ii) .......................................................... (Equation iii)
Length = 90 cm ................................................................ (From given information)
Area of a rectangle = length × breadth
∴ Area of a rectangle = 90 × 2/3 × x ...................................................... (From given information & Equation iii)
∴ Area of a rectangle = 60x .......................................................................................... (Equation iv)
We are also given that-
Area of rectangle = 4 × Area of square
∴                    60x = 4 × x² ................................................................. (From Equations i & iv)
∴                    60x = 4x²
∴                        0 = 4x² - 60x
∴                        0 = 4x (x - 15)
∴ either 4x = 0 or x - 15 = 0
∴ either x = 0 or x = 15
Since x is the side of a square, which cannot be 0, x = 15.