Question

Two sides of a square lie on the lines $x+y=1$and $x+y+2=0$ What is the area?

Answer 1

Clearly the length of the side of the square is equal to the distance between the parallel lines $x+y-1=0$ ....(i) and $x+y+2=0$ .....(ii)

Putting $x=0$ in (i) we get $y$=$1$ So $(0,1)$ is a point on line $\left(i\right)$

Now Distance between the parallel lines $=$ length of the $\perp$ from $(0,1)$ to $x+y+2=0=$ $\frac{|0+1+2|}{\sqrt{1^2+1^2}}=\frac{3}{\sqrt{2}}$

Thus the length of the side of the square is $\frac{3}{\sqrt{2}}$ and hence its area = ${\left(\frac{3}{\sqrt{2}}\right)}^2=\frac{9}{2}unit{s}^2$