If two sides of a square lie on the lines 2x+y-3=0 and 4x+2y+5=0, then what is the area of the square in square units ?

Explanation

The given lines are parallel. Divide the second line by 2 to get 2x+y+2.5=0. The side a of the square is the distance between these parallel lines 2x+y-3=0 and 2x+y+2.5=0. Thus, a = \frac{|-3 - 2.5|}{\sqrt{2^2+1^2}} = \frac{5.5}{\sqrt{5}}. The area is a^2 = \frac{30.25}{5} = 6.05 square units.

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