A square park has an area equal to the area of a rectangle whose length exceeds its breadth by 9 m and the breadth is half the side of the square. Find the side of the square.

Correct option is A

Given:
Area of square = Area of rectangle
Length of rectangle = Breadth + 9 m
Breadth of rectangle = Half of the side of the square
Formula Used:
Area of a square = side × side
Area of a rectangle = length × breadth
Solution:
Let a be the side of the square.
Express the breadth of the rectangle in terms of a:
b = $$\frac{a}{2}$$​​
Express the length of the rectangle in terms of a:
l = $$\frac{a}{2}$$​ + 9
Set the area of the square equal to the area of the rectangle:
​$$a^2 = \frac{a}{2} × (\frac{a}{2} + 9)$$​​
Expand the right side:
​$$a^2 = \frac{a^2}{4} + \frac{9a}{2}$$​​
Subtract the squared fraction from both sides:
​$$\frac{3a^2}{4} = \frac{9a}{2}$$​​
​$$\frac{3a}{4} = \frac{9}{2}$$​​
3a = 18
a = 6
Final Answer
So the correct answer is (a)