1 00:00:00,710 --> 00:00:06,850 Let's do this question in a right angle triangle, the length of the shortest median is 15 centimeter. 2 00:00:07,160 --> 00:00:13,340 If the area of the triangle is two one six square centimeter, find the length of the longest median. 3 00:00:13,730 --> 00:00:14,230 All right. 4 00:00:14,480 --> 00:00:15,400 Was the video. 5 00:00:15,590 --> 00:00:17,950 Give it a try and then let's do it together. 6 00:00:19,030 --> 00:00:21,130 All right, we're back, I hope you have given it a try. 7 00:00:21,340 --> 00:00:22,430 Let's do it together. 8 00:00:22,570 --> 00:00:24,370 Let's draw a rough sketch. 9 00:00:24,730 --> 00:00:26,960 We have a right angle triangle over here. 10 00:00:27,250 --> 00:00:33,940 Now, you can observe that the shortest median will be to the longest side and the vice versa is also 11 00:00:33,940 --> 00:00:34,320 true. 12 00:00:34,480 --> 00:00:38,200 That is the longest median will be to the shortest side. 13 00:00:39,620 --> 00:00:46,580 All right, now, this is a 90 degree angle right there for this side over here is the hypotenuse that 14 00:00:46,580 --> 00:00:48,200 is it's the longest side. 15 00:00:48,440 --> 00:00:53,200 Therefore, this median will be the shortest median right now. 16 00:00:53,210 --> 00:00:57,100 It's given that the shortest median is equal to 15 centimetre. 17 00:00:57,350 --> 00:00:57,790 Right. 18 00:00:59,440 --> 00:01:07,780 Now, let me name this triangle as triangle ABC, now AC is equal to 30 centimeters, right? 19 00:01:07,960 --> 00:01:08,810 Why is that so? 20 00:01:08,920 --> 00:01:14,840 Because we have a right angle triangle and we have drawn a median to the hypotenuse, remember? 21 00:01:14,980 --> 00:01:20,080 Therefore, if this is X, this also will be X and this also will be X. 22 00:01:20,440 --> 00:01:27,840 If I call this point a SPE, then AP is equal to pieces equal to BP because point B is these Sock'Em 23 00:01:27,850 --> 00:01:28,390 Center. 24 00:01:32,570 --> 00:01:39,470 All right, so we have found that AC is equal to 30 centimeter centimetre right now, let me call abs 25 00:01:39,470 --> 00:01:42,170 X and B C white. 26 00:01:42,170 --> 00:01:45,690 So the length of ABS X and the length of B C is white. 27 00:01:45,950 --> 00:01:53,180 Now, as per Pythagoras's theorem, we know that X squared plus Y square is equal to 30 square because 28 00:01:53,180 --> 00:01:54,590 X the hypotenuse. 29 00:01:54,590 --> 00:01:54,980 Right. 30 00:01:55,190 --> 00:02:00,560 And it's also given that the area of the triangle is two hundred and sixteen now because this is the 31 00:02:00,570 --> 00:02:05,550 right angle triangle, the altitude from point A is A itself. 32 00:02:05,780 --> 00:02:09,230 We know that the area of a triangle is half base into height. 33 00:02:09,510 --> 00:02:13,520 So the area of this triangle can be taken as 1/2 X and Y. 34 00:02:13,670 --> 00:02:15,470 That's equal to two hundred and sixteen. 35 00:02:15,680 --> 00:02:16,080 Right. 36 00:02:16,310 --> 00:02:21,560 Therefore X and Y is equal to two hundred and sixteen in the two, which is equal to four hundred and 37 00:02:21,560 --> 00:02:22,130 thirty two. 38 00:02:22,580 --> 00:02:23,020 All right. 39 00:02:23,150 --> 00:02:29,660 Now let's try to solve these two equations now before we go ahead and make it into a quadratic equation. 40 00:02:29,810 --> 00:02:33,220 We can easily solve it using trial and error substitution. 41 00:02:33,500 --> 00:02:34,780 Let's take an example. 42 00:02:35,000 --> 00:02:38,840 We know that three, four and five are forming a Pythagorean Triplette. 43 00:02:39,050 --> 00:02:39,400 Right. 44 00:02:39,650 --> 00:02:42,890 And over here, we know one side is 30 centimetre. 45 00:02:42,890 --> 00:02:44,060 That is the hypotenuse. 46 00:02:44,360 --> 00:02:48,830 So if I want to get five to 30, I need to multiply it with six. 47 00:02:48,830 --> 00:02:49,190 Right. 48 00:02:49,280 --> 00:02:51,050 So five in the six gives me thirteen. 49 00:02:51,230 --> 00:02:54,320 Now let me multiply three and four also with six. 50 00:02:54,630 --> 00:02:57,050 So that gives me 18 and twenty four. 51 00:02:57,230 --> 00:03:03,000 And let's check whether 18 and 24 satisfies X, Y is equal to 42. 52 00:03:03,350 --> 00:03:05,840 Let's try that to 18 to twenty four. 53 00:03:05,840 --> 00:03:07,530 If you do that you will get 42. 54 00:03:07,730 --> 00:03:13,790 Therefore it is satisfied and hence X and Y is equal to 18 and 24. 55 00:03:14,210 --> 00:03:14,650 All right. 56 00:03:14,900 --> 00:03:18,080 Now we need to find the length of the longest median. 57 00:03:18,350 --> 00:03:22,480 The length of the longest median will be to the shortest side. 58 00:03:22,850 --> 00:03:25,770 So let's take Y as the shortest side. 59 00:03:26,090 --> 00:03:31,070 So in that case, this will be the longest median right now. 60 00:03:31,200 --> 00:03:34,150 Let's press on to this length over here. 61 00:03:34,460 --> 00:03:39,830 That's BP is equal to nine centimetre because B is the point of B, C, right. 62 00:03:40,040 --> 00:03:42,520 Because we are talking about a median eppy. 63 00:03:42,830 --> 00:03:45,260 So we know B.C. has to be the shortest side. 64 00:03:45,470 --> 00:03:48,830 And among eighteen twenty four, eighteen is the shortest one. 65 00:03:49,040 --> 00:03:53,960 So therefore we have taken BK's 18 and we have got BP s nine. 66 00:03:54,380 --> 00:03:54,890 All right. 67 00:03:55,250 --> 00:03:57,170 Now let's proceed over here. 68 00:03:57,170 --> 00:03:59,060 We know X is equal to twenty four. 69 00:03:59,060 --> 00:03:59,510 Right. 70 00:03:59,510 --> 00:04:02,840 So let's right that over here and we have a right angle. 71 00:04:02,840 --> 00:04:06,620 Triangle A, B, B to aspart Pythagoras's theorem. 72 00:04:06,770 --> 00:04:10,850 We know a B squared is equal to twenty four squared plus nine squared. 73 00:04:11,120 --> 00:04:15,050 That gives us six hundred and fifty seven and eight. 74 00:04:15,050 --> 00:04:21,440 B will be the square root of six hundred and fifty seven and that's equal to three root seventy three. 75 00:04:21,690 --> 00:04:23,000 That is your answer.