A real brain test! Math puzzle, Can you solve It?

Let's find the area of the shaded portion or area of the space. Welcome back to my channel. This is a rectangle. Okay, this is a square. Sorry. And this particular one, we're also looking for its area is a square. Now, if this is a square, that implies, so I'll write this, that ABCD is a square. All right. now if AB is equal to BC is equal to DC is equal to AD let's call this x okay so let AD be equal to x it also means that AB is x as well right this is also x then BC is also x and DC is also x Now, if we look at this question, we are asked to find the area of this portion. Now, because this is a square as well, now, let's call this MN rather. If we say that NB is equal to y, then let every other part of this square become y. So, this is y, right? it means that from B to let's call this P from B to P is also y and from P to M let's call this portion M is also y therefore from here to here is y okay now let's try to get these parts the parts of this particular square AN will be the whole of x minus y right so we have AN is x minus y and the same thing PC will be what the whole of this is x minus y x minus y please subscribe to our channel turn on your notification bell if this is the first time you are coming across this wonderful channel give us a thumbs up if you love what we are doing and most importantly i would love to see your comment because it tells me how good the content is and also where i need correction so please comment and tell me what you feel about the video in the comment section all right now moving forward remember that a and D whatever that is here right this is a rectangle now let's call this X okay that's X let's call DC okay so a and DC is a rectangle and area area of a rectangle is equal to the length times the breadth, okay? So that means that x times x minus y will give us 15 because the area here is 15. So this implies that x multiplied by x minus y is equal to 15. Let's call this equation 1. Now, similarly, for this side, we have y multiplied by x minus y is 9. So, y multiplied by x minus y is 9. Now, let's call this equation 2. I think this is enough. Yes. Now, let's divide equation 1 by equation 2. So, equation 1 divided by 2. this implies we have x brackets x minus y over y brackets x minus y and this will be equal to 15 divided by 9 now they share something in common x minus y x minus y so this implies that x divided by y is equal to 15 divided by 9 now if we make x the subject of the formula let's cross multiply we have 9x is equal to 15 y okay now let's make um x the subject of the formula or let's make y the subject of the formula anyone so but let's go with x so dividing both sides by 9 we will have that x is equal to 15 over 9, 3 go into this 15 so we are going to have 5 over 3 y 5 over 3 y so this is our x and it is very important to write it down that x is equal to 5 over 3 y now we are going to rewrite this particular equation here okay let's do that before i erase it so we have x multiplied by x minus y is 15 and x and y multiplied by x minus y is 9 so i can now erase everything i have space all right we have 5 over 3 y as our x so i want to substitute it into the second equation i don't want to have too much and this thing to solve too much fractions to solve. So, substituting it into equation 2, we have y multiplied by, so we're going to replace x with 5 over 3y minus y is equal to 9. So, let's solve what we have inside the brackets. We have y brackets, 5y over 3 minus y over 1. Let's write it like this, and this is 9. Okay, so we have y into, the LCM of 3 and 1 is 3, right? So we can write this as 5y over 3 minus, we multiply this side by 3. And if we do that, we have 3y over 3 is equal to 9. So, now we have y brackets, 5y minus 3y, all divided by 3, is equal to 9. So, y brackets, 5y minus 3y is 2y over 3, is equal to 9. Now, if we solve for that, if you have not subscribed to the channel, you are missing something. So, I would like you to subscribe to the channel. Okay. All right. So now we have y times 2y is 2y squared divided by 3 is equal to 9. Okay. If we cross multiply, we have 2y squared is equal to 3 times 9 is 27. So we divide both sides by 2 to get y squared. So, we have y squared is equal to, 27 is 13.5 then. So, 27 will be 13.5, yeah, 13.5. Now, I'm going to stop here. Do you know why? We are asked to find the area of this square. And area of a square is length squared, right? And the length of this portion is y. Meaning that the area, area of this portion is y squared. and we have already found it from here that y squared is equal to 13.5 therefore the area is 13.5 units squared thank you so much for watching see you in my next video