Question

1.    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

The distance between two parallel lines $ax+by+c=0$ and $ax+by+d=0$

$l=\frac{|c-d|}{\sqrt{a^2+b^2}}$

So, we have $l=\frac{|c-d|}{\sqrt{a^2+b^2}}=\frac{|-10-(-5)|}{\sqrt{1^2+10^2}}=0.4975$

The area of the square $A=0.4975^2=0.2475$ . Answer