With the 'Festival of Lights' round the corner, Ketaki and Roshni decided to play a prank on the two ghosts that made
their lives miserable since the last couple of weeks. They were neighbours and their parents owned 4 houses between them.
Roshni's parents owned houses A & C while Ketaki's parents owned B and D. All four houses were perfect squares in shape.
(However, their areas did differ a bit!) The houses had a common courtyard as depicted in the figure. Each edge of the
courtyard was bounded by a wall of a different house. Ketaki called Vandana - The Ghost of CAT Past - to House B. Vandana appeared exactly at the centre of
house B. However, her appearance was sans any drama, as, this time, she had appeared during the day and the ambience was no
longer eerie. Ketaki told her that Jayshri - The Ghost of CAT Present - was waiting for her in a bottle kept at the
centre of house D. Vandana, without thinking, fell prey to innocent-looking Ketaki's clever subterfuge. The moment she
entered the bottle, Roshni - who was hiding behind a couch in house D, corked the bottle. After that, Roshni summoned Jayshri
to House A and told her that Ketaki was waiting for her in a bottle kept exactly at the centre of House C. Jayshri, like
Vandana, did not suspect Roshni's intentions and immediately rushed from the centre of house A to the centre of house C. She,
too, got trapped in one swift move. The girls traced the paths taken by Jayshri and Vandana by black and blue rangoli colours
respectively. They kept the two bottles at the intersection point of the two paths. Said Ketaki,
"Hahahaha!!! You foolish ghosts. You may be good at math but it doesn't look like you'll interpret data too well." Roshni
sniggered. "You two have been terrifying us for quite a while now. It's time for some payback!!! We'll let you go if you
answer one simple question. I think that the paths taken by you two were unequal. However, Roshni here begs to differ. She
says you two traced equally long paths. Now tell us who's right- Me or Roshni? If you can't answer the question, you will
spend Diwali in this bottle and will be let out only when we light rockets!!! You have exactly an hour until take off
Help them figure out a solution. Provide a detailed solution along with your answer.