1 00:00:00,740 --> 00:00:05,530 Let's do this question in a triangle, the longest side is 20 centimeter. 2 00:00:05,940 --> 00:00:07,930 Another side is 15 centimeter. 3 00:00:08,300 --> 00:00:11,450 The area of the triangle is 90 square centimeter. 4 00:00:11,690 --> 00:00:13,010 Find the third side. 5 00:00:13,410 --> 00:00:13,840 All right. 6 00:00:14,000 --> 00:00:20,050 So we have BK's equal to 20 abs, equal to 15, and we need to find the value of AC. 7 00:00:20,240 --> 00:00:20,710 All right. 8 00:00:20,960 --> 00:00:24,470 Pause the video, give it a try, and then let's do it together. 9 00:00:25,040 --> 00:00:25,520 All right. 10 00:00:25,520 --> 00:00:26,010 We're back. 11 00:00:26,180 --> 00:00:27,560 I hope you've given it a try. 12 00:00:27,770 --> 00:00:28,890 Let's do it together. 13 00:00:29,210 --> 00:00:33,320 Let's drop a perpendicular from point A to cite B, C. 14 00:00:35,270 --> 00:00:41,240 All right, this is our height and let this point be OK now we have seen that the area of the triangle 15 00:00:41,240 --> 00:00:41,900 is half. 16 00:00:42,820 --> 00:00:44,830 Based in the height. 17 00:00:45,850 --> 00:00:52,840 Right over here, let's take 20 as the base, if you take 20 as the base, then the height is this length 18 00:00:52,840 --> 00:00:53,850 over here, right? 19 00:00:54,010 --> 00:00:57,310 It's the perpendicular distance from the opposite vertex. 20 00:00:57,520 --> 00:01:04,690 To decide if I was to take a B as the base, then the height would be the perpendicular distance from 21 00:01:04,690 --> 00:01:07,740 point C to side A B, right. 22 00:01:07,900 --> 00:01:14,020 And if I have to take AC as the base, the height would be the perpendicular distance from point B to 23 00:01:14,020 --> 00:01:14,830 side easy. 24 00:01:15,130 --> 00:01:21,790 All right, now let's move on or here we are taking B.C. as the base and the height is the perpendicular 25 00:01:21,790 --> 00:01:27,880 distance from point A, which is the opposite vertex to B.C. And we have marked it as it's now it's 26 00:01:27,880 --> 00:01:35,730 given that the area is equal to 90 square centimeter, therefore half in twenty two is equal to ninety. 27 00:01:36,190 --> 00:01:39,550 So I can cut out two from the numerator and the denominator. 28 00:01:39,760 --> 00:01:42,700 So I get X equal to nine centimeter. 29 00:01:43,090 --> 00:01:43,600 All right. 30 00:01:44,230 --> 00:01:47,720 Now A B or is it right angled triangle. 31 00:01:47,830 --> 00:01:48,170 Right. 32 00:01:48,190 --> 00:01:53,560 You can see that this angle over here is a 90 degree angle because that's how we take the height. 33 00:01:53,830 --> 00:02:01,020 And as per Pythagoras's theorem, we can find that 15 square is equal to eight squared plus or B square, 34 00:02:01,390 --> 00:02:03,610 and we have found that it is equal to nine. 35 00:02:03,790 --> 00:02:07,090 So 15 squared is equal to nine squared plus or B squared. 36 00:02:07,390 --> 00:02:09,100 15 squared is 225. 37 00:02:09,490 --> 00:02:10,880 Nine squared is eighty one. 38 00:02:11,290 --> 00:02:15,790 So 225 minus eighty one gives you one forty four. 39 00:02:15,970 --> 00:02:22,600 Therefore Albe Square is equal to one forty four or B is equal to square root of one forty four which 40 00:02:22,600 --> 00:02:23,710 is equal to twelve. 41 00:02:24,070 --> 00:02:24,520 All right. 42 00:02:24,730 --> 00:02:32,110 But we have found that obese 12, we know BK's 20, therefore C will be twenty minus twelve which is 43 00:02:32,110 --> 00:02:33,580 equal to eight centimetre. 44 00:02:33,970 --> 00:02:35,920 Now let's mark that over here. 45 00:02:36,040 --> 00:02:41,860 We have Oak's eight centimetre now a C or is also a right angle triangle. 46 00:02:41,860 --> 00:02:42,220 Right. 47 00:02:42,370 --> 00:02:46,300 Therefore ASBA Pythagoras's Theorem X squared is equal to. 48 00:02:47,370 --> 00:02:50,740 It's square or a square plus orthey square. 49 00:02:50,910 --> 00:02:54,090 We know it his name and we have found all eight. 50 00:02:54,270 --> 00:02:57,210 Therefore Square is nine square plus eight square. 51 00:02:57,390 --> 00:03:01,230 That's eighty one plus sixty four, which is equal to one forty five. 52 00:03:01,440 --> 00:03:04,500 Therefore X equals the square root of one forty five. 53 00:03:04,680 --> 00:03:06,510 And that's approximately 12. 54 00:03:06,510 --> 00:03:06,810 Right. 55 00:03:06,900 --> 00:03:12,210 Because we know 12 square is equal to one forty four, which is very close to one forty five. 56 00:03:12,870 --> 00:03:14,190 And that is your answer.