1 00:00:00,790 --> 00:00:03,590 Let's do this question in the figure below. 2 00:00:03,790 --> 00:00:10,840 Find the sum of the ingredients of Triangle B, Q, R and Triangle P, as are. 3 00:00:11,200 --> 00:00:11,710 All right. 4 00:00:11,950 --> 00:00:12,840 Was the video. 5 00:00:13,030 --> 00:00:15,400 Give it a try and then let's do it together. 6 00:00:15,970 --> 00:00:16,390 All right. 7 00:00:16,390 --> 00:00:16,900 We're back. 8 00:00:16,930 --> 00:00:17,940 Let's do it together. 9 00:00:18,310 --> 00:00:18,820 Over here. 10 00:00:18,820 --> 00:00:19,600 You can see that. 11 00:00:19,600 --> 00:00:22,140 Twenty, fifteen and twenty five. 12 00:00:22,390 --> 00:00:24,880 That is the three sides of triangle P. 13 00:00:24,880 --> 00:00:28,180 Q is form a Pythagoras triplet. 14 00:00:28,180 --> 00:00:28,600 Right. 15 00:00:28,820 --> 00:00:29,700 Why is that so. 16 00:00:30,100 --> 00:00:34,870 The first reason is you can see twenty five squared is equal to twenty squared plus fifteen squared. 17 00:00:35,290 --> 00:00:35,680 Right. 18 00:00:36,070 --> 00:00:40,450 And we have discussed other numbers how to find quickly squares of numbers. 19 00:00:40,750 --> 00:00:41,100 Right. 20 00:00:41,320 --> 00:00:46,090 And there is also a different way in which you can find that this is a Pythagoras triplet. 21 00:00:46,390 --> 00:00:52,470 You can quickly observe that it's related to the Pythagorean Triplette five, four, three. 22 00:00:52,810 --> 00:00:57,250 Now take this Pythagoras Triplette and multiply throughout with five. 23 00:00:58,390 --> 00:01:04,630 So over here, five into five gives you twenty five or in the five gives you twenty and three in the 24 00:01:04,630 --> 00:01:05,740 five gives you fifteen. 25 00:01:05,980 --> 00:01:11,950 So we have already seen that if you take it by the intraplate and multiply it throughout with the number, 26 00:01:12,100 --> 00:01:14,080 you will get another by the intraplate. 27 00:01:14,470 --> 00:01:14,950 All right. 28 00:01:15,100 --> 00:01:21,160 Now having established that twenty fifteen and twenty five former Pythagorean Triplette, therefore 29 00:01:21,160 --> 00:01:25,240 Angle Kupets will be a 90 degree angle, right. 30 00:01:25,570 --> 00:01:27,420 This angle will be a 90 degree angle. 31 00:01:28,180 --> 00:01:31,330 Let's mark the length B are as it's. 32 00:01:32,350 --> 00:01:37,900 All right, now we know that the area of a triangle is equal to half base in height. 33 00:01:38,300 --> 00:01:44,380 Now let's take 15 as the base, then 20, that is space would be the height, right? 34 00:01:44,420 --> 00:01:47,080 If BQ is the base B, as is the height. 35 00:01:47,320 --> 00:01:52,270 So I can right the area of this triangle as half in the 15 or 20. 36 00:01:52,570 --> 00:01:57,220 Or if Q is the base then P R is the height. 37 00:01:57,220 --> 00:01:57,490 Right. 38 00:01:57,490 --> 00:02:03,510 Because this angle has to be 90 degrees over your base is the height because this angle is 90 degrees. 39 00:02:03,760 --> 00:02:04,170 All right. 40 00:02:04,300 --> 00:02:07,180 So if QSA is the base bar is the height. 41 00:02:07,190 --> 00:02:12,810 So they African wilderness often took us into B-R or it's all right. 42 00:02:12,820 --> 00:02:13,720 So let's right that. 43 00:02:13,940 --> 00:02:20,860 So I have half in the 15 and 20, which is the area and we also have half in to us. 44 00:02:20,860 --> 00:02:23,580 That's twenty five in the edge as the area. 45 00:02:23,800 --> 00:02:30,160 Therefore I can equate these two expressions because it's giving us the same area that is the area of 46 00:02:30,160 --> 00:02:31,460 Triangle Kupets. 47 00:02:31,840 --> 00:02:32,350 All right. 48 00:02:32,500 --> 00:02:37,710 Now using this equation, I can find that it is equal to twelve, right? 49 00:02:37,930 --> 00:02:39,700 Often half gets cancelled out. 50 00:02:39,970 --> 00:02:41,590 Over here you have 15. 51 00:02:41,770 --> 00:02:46,810 So you divide it by five, you get three to divide this by fire, you get five and five. 52 00:02:47,590 --> 00:02:49,870 Cut it out from both sides and you're left with four. 53 00:02:50,080 --> 00:02:55,300 So you get it is equal to three in the four, which is equal to twelve to the height over here is twelve 54 00:02:55,300 --> 00:02:56,010 centimeter. 55 00:02:56,260 --> 00:02:56,710 All right. 56 00:02:56,920 --> 00:03:01,420 Now let's take a triangle to our peak. 57 00:03:01,760 --> 00:03:05,620 The Triangle Q, r B is also a right angle triangle. 58 00:03:05,620 --> 00:03:06,040 Right. 59 00:03:06,220 --> 00:03:13,740 Therefore side Q are can be found as root of 15 square minus 12 square. 60 00:03:14,010 --> 00:03:15,150 That gives you nine. 61 00:03:15,340 --> 00:03:16,130 Why is that so. 62 00:03:16,300 --> 00:03:18,280 Because this is the hypotenuse. 63 00:03:18,280 --> 00:03:18,640 Right. 64 00:03:18,830 --> 00:03:24,610 But we know 15 square is equal to Q are squared plus it's square and that is twelve. 65 00:03:24,610 --> 00:03:24,880 Right. 66 00:03:25,210 --> 00:03:25,990 Well squared. 67 00:03:25,990 --> 00:03:28,630 So take this to the other side and you get. 68 00:03:28,630 --> 00:03:30,790 Q What is the square root of 15 square. 69 00:03:30,790 --> 00:03:36,390 Minus 12 square that gives you eighty one and square root of eighty one gives you nine. 70 00:03:36,400 --> 00:03:42,280 So QR is equal to nine, therefore ours would be twenty five minus nine. 71 00:03:42,280 --> 00:03:42,670 Right. 72 00:03:42,820 --> 00:03:44,770 Which is equal to sixteen. 73 00:03:45,700 --> 00:03:46,270 All right. 74 00:03:46,450 --> 00:03:48,630 Now we have established this over here. 75 00:03:48,910 --> 00:03:50,000 Let me right this over here. 76 00:03:50,040 --> 00:03:53,440 Q Are is nine and ours is equal to sixteen. 77 00:03:53,740 --> 00:03:55,480 So let's take this aside. 78 00:03:56,740 --> 00:03:59,840 All right, now let me market over here again. 79 00:03:59,860 --> 00:04:07,480 We have nine and 16 over here and it is equal to 12 already in triangle because you are in this triangle. 80 00:04:07,690 --> 00:04:12,610 You can see that half you are into it will give you the area. 81 00:04:12,610 --> 00:04:14,760 Right, because this angle is 90 degrees. 82 00:04:14,920 --> 00:04:20,070 Therefore, half base in the height is the area that is half you are into it. 83 00:04:20,470 --> 00:04:27,970 And we have seen that the area of a triangle can also be found as the product of the in radius and the 84 00:04:27,970 --> 00:04:29,010 semi perimeter. 85 00:04:29,290 --> 00:04:41,240 So of you are into it is equal to our into S1 where R-1 is the semi inside Iran is the radius of triangle. 86 00:04:41,560 --> 00:04:45,490 You are an S1 is the same perimeter of trying to pick you up. 87 00:04:45,820 --> 00:04:46,300 All right. 88 00:04:46,420 --> 00:04:53,230 So let's substitute the values that gives us nine by two in the 12th is equal to 18 into our. 89 00:04:53,500 --> 00:04:55,480 As one is equal to 18. 90 00:04:55,480 --> 00:04:55,720 Right. 91 00:04:55,750 --> 00:04:59,410 How do you find that 15 plus nine plus 12. 92 00:04:59,680 --> 00:05:01,810 That gives you 36. 93 00:05:01,810 --> 00:05:02,170 Right. 94 00:05:02,260 --> 00:05:03,340 And 36 by two. 95 00:05:03,340 --> 00:05:04,810 Gives you 18. 96 00:05:06,000 --> 00:05:08,250 All right, let's press on. 97 00:05:08,460 --> 00:05:12,620 So from this equation, we can find that R-1 is equal to three. 98 00:05:12,900 --> 00:05:17,110 So the radius of Triangle Park you are is equal to three centimeter. 99 00:05:17,520 --> 00:05:19,920 Similarly, let's take triangle B. 100 00:05:19,920 --> 00:05:20,280 R. 101 00:05:20,280 --> 00:05:20,640 S. 102 00:05:20,940 --> 00:05:29,040 We can ride off into 16 and 12 is equal to our two in the S2 and S2 is equal to forty eight by two, 103 00:05:29,220 --> 00:05:30,840 which gives you twenty four. 104 00:05:30,870 --> 00:05:31,230 Right. 105 00:05:31,380 --> 00:05:37,740 So using this equation you can find that our two is equal to four centimetre and you are asked to find 106 00:05:37,740 --> 00:05:39,810 the sum of the radiuses. 107 00:05:40,020 --> 00:05:44,190 So that would be R one plus R two which is equal to three plus four. 108 00:05:44,400 --> 00:05:47,270 That gives you the answer seven centimetre. 109 00:05:47,820 --> 00:05:53,000 Now in the next video we learn a shortcut to do the same thing much faster.