1 00:00:00,680 --> 00:00:07,880 Let's do this question, Esquire is inscribed in a circle of cites 13, 15 and four centimetre. 2 00:00:08,210 --> 00:00:12,410 One of the sides of the square lies on the longest side of the triangle. 3 00:00:12,710 --> 00:00:17,210 The other two vertices of the square, that's the other side of the triangle. 4 00:00:17,390 --> 00:00:18,750 Find the length of the square. 5 00:00:18,920 --> 00:00:19,360 All right. 6 00:00:19,370 --> 00:00:22,470 Pause the video, give it a try and then let's do it together. 7 00:00:22,850 --> 00:00:23,300 All right. 8 00:00:23,300 --> 00:00:23,790 We are back. 9 00:00:23,930 --> 00:00:25,000 Let's do it together. 10 00:00:25,490 --> 00:00:26,050 Over here. 11 00:00:26,060 --> 00:00:30,670 I have my triangle and it's mentioned that the square is placed. 12 00:00:30,830 --> 00:00:35,480 That's that it's one side is on the longest side of the triangle. 13 00:00:35,690 --> 00:00:38,990 So let's mark the sides and the partisans of the triangle. 14 00:00:39,410 --> 00:00:41,140 Now, this has to be 15. 15 00:00:41,150 --> 00:00:42,340 That is the longest side. 16 00:00:42,500 --> 00:00:43,940 And let's take this as 13. 17 00:00:43,940 --> 00:00:46,700 And this has four at these points, B, ABC. 18 00:00:46,940 --> 00:00:50,030 Now let's mark the citizens of the square as P. 19 00:00:50,030 --> 00:00:55,250 Q are and s now we need to find the length of the square right now. 20 00:00:55,260 --> 00:01:01,220 What is the same perimeter of this triangle that would be 15 plus four plus thirteen by two, which 21 00:01:01,220 --> 00:01:02,300 is equal to sixteen. 22 00:01:02,540 --> 00:01:07,000 Now we know how to find the area of a triangle if you know the three sites as. 23 00:01:07,010 --> 00:01:08,150 But heroin's formula. 24 00:01:08,150 --> 00:01:08,450 Right. 25 00:01:08,600 --> 00:01:15,500 That would be square root of S in S minus in the S minus B into S minus C. 26 00:01:15,500 --> 00:01:15,840 Right. 27 00:01:15,980 --> 00:01:17,400 So let's apply that over here. 28 00:01:17,630 --> 00:01:19,370 You get the area as. 29 00:01:20,690 --> 00:01:28,580 Square root of sixteen into one, into 12 into three, that is equal to twenty four to the area of triangle, 30 00:01:28,580 --> 00:01:31,150 ABC is equal to twenty four. 31 00:01:31,290 --> 00:01:35,090 All right, now let me draw a perpendicular to Vertex eight. 32 00:01:35,480 --> 00:01:36,950 So that's the altitude. 33 00:01:37,100 --> 00:01:43,550 And let me take that as it's the area also can be found as 15 in to it's by two. 34 00:01:43,550 --> 00:01:46,550 Right, because it is half into base, into height. 35 00:01:46,700 --> 00:01:49,220 Now this has to be equal to twenty four. 36 00:01:49,310 --> 00:01:56,270 So let me get this to twenty four and I get that the height that is edge over here will be equal to 37 00:01:56,270 --> 00:01:57,770 16 by five. 38 00:01:58,100 --> 00:01:58,550 All right. 39 00:01:58,760 --> 00:02:02,630 Now let this height over here be êtes to. 40 00:02:04,140 --> 00:02:06,140 That is the height of a barbecue. 41 00:02:06,180 --> 00:02:08,310 All right, so let this be it, too. 42 00:02:08,620 --> 00:02:16,740 Now you can see that triangle ABC and Triangle EPICA, that is this smaller triangle and this big triangle 43 00:02:16,740 --> 00:02:18,240 are similar, right? 44 00:02:18,420 --> 00:02:19,360 Why is that so? 45 00:02:19,560 --> 00:02:22,320 Because this angle will be equal to this angle. 46 00:02:22,500 --> 00:02:26,340 This angle will be equal to this angle over here right now. 47 00:02:26,370 --> 00:02:27,070 Why is that so? 48 00:02:27,090 --> 00:02:28,270 Can you tell me why that is? 49 00:02:28,470 --> 00:02:32,510 We know that this side is parallel to the side because this is a square, right. 50 00:02:32,700 --> 00:02:39,600 So this angle over here has to be equal to this angle because this side is lying on ABC. 51 00:02:39,610 --> 00:02:41,760 That means BQ is parallel to ABC. 52 00:02:41,970 --> 00:02:44,520 Therefore, these two angles are corresponding angles. 53 00:02:44,770 --> 00:02:48,060 Similarly, this angle on this angle are also corresponding angles. 54 00:02:48,460 --> 00:02:54,390 That's why Triangle ABC is similar to triangle apical Asper aerial. 55 00:02:54,630 --> 00:02:55,110 All right. 56 00:02:55,920 --> 00:02:56,760 So these two. 57 00:02:57,700 --> 00:03:02,260 Angles are equal and we have these two angles as equal. 58 00:03:02,620 --> 00:03:09,660 All right, now over here, this angle is a common angle right now because these two triangles are similar. 59 00:03:09,790 --> 00:03:18,430 We can say that it's too divided by eight is equal to a divided by B.C. Right now, I'm taking the side 60 00:03:18,430 --> 00:03:21,160 of the square as two to sword to divide it by. 61 00:03:21,160 --> 00:03:23,320 It is equal to a divided by B.C.. 62 00:03:23,620 --> 00:03:24,880 Now we know that. 63 00:03:25,790 --> 00:03:32,600 It's too can be written as 16 by five minus eight, right? 64 00:03:32,630 --> 00:03:33,510 Why is that so? 65 00:03:33,920 --> 00:03:36,010 Six by five is it? 66 00:03:36,260 --> 00:03:40,310 And this land over here will be equal to it because this is a square. 67 00:03:40,310 --> 00:03:40,640 Right. 68 00:03:40,730 --> 00:03:44,770 So therefore, it's two has to be 16 by five minus eight. 69 00:03:44,780 --> 00:03:45,150 Right. 70 00:03:45,380 --> 00:03:51,950 So let's right that over here, 16 by five minus eight divided by 16 by five, which is which is equal 71 00:03:51,950 --> 00:03:53,260 to a by 15. 72 00:03:53,390 --> 00:03:53,680 Right. 73 00:03:53,870 --> 00:03:55,250 Because equal to 15. 74 00:03:55,550 --> 00:03:57,610 Now over here, let's solve for it. 75 00:03:57,770 --> 00:04:06,200 We get sixteen minus five by sixteen is equal to about 15 or we get ninety one is equal to 240 or is 76 00:04:06,200 --> 00:04:08,540 equal to 240 by ninety one. 77 00:04:08,540 --> 00:04:13,490 And that is the answer to this question because we have to find the length of the square.