Geometry math challenge| area

Let's solve this tricky geometrical math problem. So, we are asked to find the area of this square if the length of this side is 16 and the length of this side is 24. Now, we are going to start from what we are asked to do. We are asked to find the area of this square. The area of a square is the length squared, right? So, first of all, our area is equal to the square of the length. Now, let our L be equal to X. So, the length of this square, let's call it X. So, it means that here is X, here is X, here is X, and here is X as well. Now, if we say that this is X and the distance from here to here is 16, That means the part on this side, from here to here, will be 16 minus X, right? So, we have 16 minus X here. Now, this is a right angle. Yes, this is a right angle. Yes, this is a right angle. You can see that. Alright, now let us look at this particular one. If we say that from here to here is 24, it means that from here to here will be 24 minus X. So, we have here as 24 minus X. Yes. Now, where am I going? Where am I heading? If you look at this, since this line and this line are perpendicular, that is, this is a straight line and this is a straight line, It means that two of them can never meet each other when you draw them. So, they are parallel to each other. Once this line is parallel to this line, it means that these two triangles have formed similar triangles. Now, that means we have similar triangles. This is the first one. We have 16 minus X here. And this is X. And this is the second one. Okay, we have 24 minus X here. And this is our X for the second triangle. Now, where am I heading with this? If these two triangles are similar, then the ratios of their corresponding sides are(datasets) It means that we can express their ratio in this manner. So, if we say 16 minus X divided by X, that is, 16 minus X divided by X should be equal to X divided by this. X divided by 24 minus X. Alright, so at this point, let us cross-multiply. Okay, before that, click the subscription button and turn on the notification bell if this is the first time you have seen this lovely shadow and this lovely face as well. Yes, okay. And thank you so much for joining. Give us a thumbs up if you're actually enjoying this video. If you're a returning viewer or a returning subscriber, thank you so much for your support. I really appreciate it. Okay, now look at this. Let us cross multiply. Now, we have X times X is X squared. Remember that we are trying to find the value of X so that we can determine our area. Okay, since our length is X. Now, X squared is equal to 16 minus X multiplied by 24 minus X. Now, if we expand this, we have X squared equals 16 times 24, right? Yeah, then 16 times minus X, which is minus 16X. Then minus X times 24 is minus 24X. And minus X times minus X is plus X squared. So we have X squared equal to 16 multiplied by 24. Then minus 16X minus 24X will give us minus 40X, right? So we have minus 40X plus X squared. Now, if we combine like terms, let's subtract x squared from both sides of this equation. So we have X squared minus X squared equal to 16 multiplied by 24 minus 40X plus X squared minus X squared. So you can see that X squared will cancel X squared, and X squared minus X squared is also zero from here. Okay, so what we have now is, I think we've already used this. Okay, so what we have now is X squared minus X squared equals zero. So we have zero equal to 16 multiplied by 24 minus 40X. Okay, now let's bring this 40X over to this side to eliminate the negative sign. So we add 40X to both sides. Okay, so zero plus 40X equals this one, this side plus 40X. So this will cancel this. So we have zero plus 40X, which gives us 40X equals 16 multiplied by 24. Now let's divide both sides. Divide both sides by 40. Okay, so if we do that, we will have 40X divided by 40 equal to 16 multiplied by 24 divided by 40. Now 40, we divide 40, we have X equals. Now let's divide by 4. When 4 divides 16, we get 4. Divide 40, we get 10. When 2 divides 4, we get 2. Dividing this, we get 5. So what we have is 2 times 24, which is 48 divided by 5, which is equal to. 48 divided by 5 gives us 9 with a remainder of 3. The 3 adds 0, 30. Divided by 5, we have 6. So it means our X is 9.6. Amazing, right? Now, the equation indicates that we should find the area of this specific region. Okay, now the area of this portion is, remember that the area is L squared. That means area is, remember, our L is X, X squared. So that means the area is 6.9 squared, right? I mean 9.6 squared, sorry, is 9.6 squared. Alright, now to settle this, let's first solve. This means 9.6 multiplied by 9.6. Now let's ignore the decimal point and solve this as 96 multiplied by itself. That is 96 squared. We'll place our decimal point afterward. Okay, so 96 squared, 6 squared is 36. Nine squared is 81. I'm going to apply a math trick here. If you'd like to see in detail how I solve this, check out the math tricks on my channel, okay? I have a playlist for it. Alright, so we have 8, 1, 3, 6. That is, 6 squared is 36. 9 squared is 81. Now 9 times 6 is 54. 54 times 2 is 108. So we add 8 here. Okay, we have 6, carry 1. We have 2, we have 9. Now remember that we have two decimal places here. So 1, 2. So this becomes our answer, square meters. Alright, so the area of this shaded region is 92.16 square meters. Thank you so much for watching. See you in my next video. Bye.