1 00:00:00,590 --> 00:00:07,400 Let's do this question, two opposite sides of a square given by the equations, three X plus four Y 2 00:00:07,400 --> 00:00:12,280 minus 10 is equal to zero and three X plus four Y plus 20 equals zero. 3 00:00:12,650 --> 00:00:15,200 Find the length of the diagonal of the square. 4 00:00:15,470 --> 00:00:15,920 All right. 5 00:00:16,160 --> 00:00:17,080 What's the video? 6 00:00:17,180 --> 00:00:19,560 Give it a try and then let's do it together. 7 00:00:19,910 --> 00:00:20,330 All right. 8 00:00:20,330 --> 00:00:20,760 We're back. 9 00:00:20,780 --> 00:00:21,720 Let's do it together. 10 00:00:21,980 --> 00:00:24,030 So let me draw a rough sketch over here. 11 00:00:24,260 --> 00:00:25,800 I have a square over here. 12 00:00:26,000 --> 00:00:29,280 Let me name it as A, B, C, D. 13 00:00:29,720 --> 00:00:36,440 OK, so now you can notice that the side of the square will be equal to the distance between two sides. 14 00:00:36,440 --> 00:00:36,710 Right. 15 00:00:36,980 --> 00:00:43,160 So, for example, if I find the distance between A, B and C, that would be equal to the side of the 16 00:00:43,160 --> 00:00:43,570 square. 17 00:00:43,700 --> 00:00:44,050 Right. 18 00:00:44,210 --> 00:00:45,650 Because all the sides are equal. 19 00:00:45,680 --> 00:00:48,230 So I just need to find the distance between two sides. 20 00:00:48,590 --> 00:00:49,050 All right. 21 00:00:49,250 --> 00:00:52,160 So I am given over here to equations of lines. 22 00:00:52,160 --> 00:00:52,550 Right. 23 00:00:52,550 --> 00:00:53,930 That are opposite to each other. 24 00:00:54,090 --> 00:00:59,760 And we know that opposite sides in a square are parallel to each other because a square is a parallel. 25 00:01:00,320 --> 00:01:03,430 Now we know how to find the distance between two parallel lines. 26 00:01:03,650 --> 00:01:09,340 That would be C one minus two divided by square root of A squared plus B square. 27 00:01:09,370 --> 00:01:09,650 Right. 28 00:01:09,770 --> 00:01:11,640 And you always take the positive value. 29 00:01:11,870 --> 00:01:13,270 So let's apply that over here. 30 00:01:13,430 --> 00:01:19,500 You get twenty minus minus ten divided by square root of three squared plus four square. 31 00:01:19,520 --> 00:01:21,280 Right over here you have 20. 32 00:01:21,440 --> 00:01:22,400 That's your C one. 33 00:01:22,550 --> 00:01:24,260 And over here you have minus 10. 34 00:01:24,440 --> 00:01:25,640 That's your C two. 35 00:01:25,640 --> 00:01:25,880 Right. 36 00:01:25,910 --> 00:01:31,040 So twenty minus minus ten divided by root of three squared plus four square threes. 37 00:01:31,040 --> 00:01:33,440 Your eight and four is your beat. 38 00:01:33,650 --> 00:01:37,790 Now this simplifies to 30 divided by five which is equal to six. 39 00:01:38,060 --> 00:01:42,710 Now if your option in the question was six, don't hurry to mark the answer. 40 00:01:42,750 --> 00:01:47,750 Six, because over here we are asked to find the length of the diagonal of the square. 41 00:01:47,760 --> 00:01:48,080 Right? 42 00:01:48,320 --> 00:01:53,480 So if the side of the square is six units, then the diagonal would be six root two. 43 00:01:53,480 --> 00:01:53,810 Right. 44 00:01:53,960 --> 00:01:54,490 Why is that? 45 00:01:54,500 --> 00:01:56,310 So we have to save six. 46 00:01:56,360 --> 00:01:58,580 And this angle is a 90 degree angle. 47 00:01:58,760 --> 00:02:04,610 Therefore, Asper Pythagoras's theorem this side over here, which is a diagonal, will be root of six 48 00:02:04,610 --> 00:02:07,520 squared plus six square, which is equal to six through to.