Question

Two sides of a square are on the line x + 10y – 10 = 0 and x + 10y – 5 = 0. Find the area of the square.

Answer 1

It is obvious that these lines are parallel, then by the formula of the distance between the lines we will find the side of the square:

$\text{For }Ax+By+D_1=0\text{ and }Ax+By+D_2=0\text{:}$

$a=\frac{|D_1-D_2|}{\sqrt{A^2+B^2}}=\frac{|-10+5|}{\sqrt{1+100}}=\frac{5}{\sqrt{101}}$

$S=a^2=\frac{25}{101}$