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.
Show answer & explanation
Correct answer: A
Explanation
Given:
Length of the rectangle = Width + 9
Width of the rectangle = Side of the square / 2
According to the formula:
Area (Square) = Area (Rectangle)
Let the side of the square = x
Width of the rectangle = x/2
Length of the rectangle = x/2 + 9
x² = (x/2)(x/2 + 9)
= x²/4 + 9x/2
⇒ x² − x²/4 − 9x/2 = 0
⇒ (3x²/4 − 9x/2) = 0
⇒ (3x² − 18x)/4 = 0
⇒ 3x(x − 6) = 0
x = 6 meters