How to solve this viral math problem - By tecmath
Transcript
00:00 | Good day and welcome to Tech Math Channel . I'm | |
00:02 | josh , Consider this problem and see if you can | |
00:04 | solve it . We're starting with a rectangle here and | |
00:07 | with this rectangle , we have three circles within it | |
00:09 | . We have this large circle here that has a | |
00:11 | diamond of six units . We have a medium sized | |
00:13 | circle up against it that has a diamond of four | |
00:16 | units . And we have this small circle here . | |
00:18 | Up against that That has a diameter of three units | |
00:21 | . This is our problem . We're trying to work | |
00:23 | out the distance between these two points here between the | |
00:26 | sixth circle and the three circle . What is this | |
00:29 | distance ? So pause this video . If you'd like | |
00:31 | to give this problem and try and when you're ready | |
00:33 | to keep watching and learn how to solve this problem | |
00:35 | started up again . Okay , so time's up . | |
00:48 | Did you manage to solve it ? Well , if | |
00:50 | you did , Congratulations . If not , I'm going | |
00:52 | to go through the answer right now . So the | |
00:54 | first thing we're going to do to solve this problem | |
00:56 | is we are going to mark on the centers of | |
00:59 | each of our circles here . We're going to use | |
01:01 | east for guides to make two right angle triangles , | |
01:04 | which are going to help us work out the distance | |
01:06 | . First right angle triangle is this one here we | |
01:09 | have two sides that form the right angle and we | |
01:13 | have the high pot news which goes right there . | |
01:15 | The first one we can work out is this high | |
01:17 | Polynesia , We know that the radius of this particular | |
01:21 | circle is half the diameter , so it's going to | |
01:23 | be equal to two . We know that the radius | |
01:26 | of this particular circle is going to be half of | |
01:28 | this diameter , so it is going to be equal | |
01:30 | to three . So we can work out the total | |
01:32 | distance of the high pot news two plus three is | |
01:35 | equal to five . The next thing we can do | |
01:37 | is work out the distance on the shorter side . | |
01:40 | We know that the distance from the center to the | |
01:43 | edge here is equal to three . We know that | |
01:45 | the distance on this circle from the center to the | |
01:47 | edge is equal to two . So therefore our length | |
01:51 | is going to be , the difference between these three | |
01:54 | . Take away two is equal to one . What | |
01:57 | we're going to be trying to find out is this | |
01:59 | unknown side length here . So that's the first triangle | |
02:02 | that we're going to be using . The next step | |
02:04 | in solving this problem is to construct a second right | |
02:07 | angle triangle as follows . So we have the two | |
02:10 | sides that meet to give the right angle just here | |
02:13 | between these two center points , we have this high | |
02:17 | pot news . So first off , what we can | |
02:18 | do is we can work out the distance of this | |
02:21 | high pot news , we know from the center of | |
02:23 | this circle to the edge . It has a radius | |
02:27 | of two . We know in a smaller circle here | |
02:29 | , from the center to the edge , it has | |
02:31 | a radius of 1.5 . So our high pot news | |
02:34 | is going to be the some of these , we're | |
02:35 | going to add them together . 1.5 plus two gives | |
02:38 | us a high pot news of 3.5 . We can | |
02:42 | also work at the height of this triangle fairly simply | |
02:44 | as follows . We know that the radius of this | |
02:47 | circle here is 1.5 . We know that the radius | |
02:52 | of this circle here is equal to two . So | |
02:55 | we know the entire distance from here to here is | |
02:59 | equal to six . So six takeaway to take away | |
03:02 | 1.5 . This gives us a height here of 2.5 | |
03:08 | . So now what we can do is work out | |
03:10 | this second distance along here and you're going to see | |
03:12 | that the sum of these two distances is going to | |
03:14 | be equal to our unknown distance that we're trying to | |
03:17 | work out . So let's work them out right now | |
03:20 | and finish solving this problem . It's pretty easy . | |
03:22 | We're going to use Pythagoras theorem , which is as | |
03:24 | follows , it says for any right angle triangle , | |
03:27 | which I've just drawn down here , it has to | |
03:30 | shorter length , which are A B and a longer | |
03:33 | high pot news , which is equal to see . | |
03:36 | And Pythagoras theorem says the following the A squared plus | |
03:40 | B squared for this triangle , the sum of the | |
03:42 | two shorter length squared is equal to the length of | |
03:46 | the hypotenuse squared A squared plus B squared equals c | |
03:49 | squared . So we're going to use this particular equation | |
03:53 | here . Just a bit jumbled around . So the | |
03:55 | first one that we have here , we have the | |
03:57 | side lengths , A , B and C . We | |
04:01 | can now substitute in to the formula here , A | |
04:04 | squared which is one squared plus X squared is equal | |
04:09 | to five squared one squared one times one is equal | |
04:13 | to one . Plus X squared is equal to five | |
04:17 | squared which is five times five , which is equal | |
04:19 | to 25 . So this therefore means that X squared | |
04:23 | is equal to 25 . Subtract one , X squared | |
04:27 | is equal to 24 . Therefore X is equal to | |
04:32 | the square root of 24 . This can be simplified | |
04:35 | further as follows . Two square root six . To | |
04:38 | work out our second triangle here , we're going to | |
04:40 | use A squared plus B squared equals c squared . | |
04:43 | Once again we have a . We have B and | |
04:46 | we have seen the two shorter length and this longer | |
04:49 | length here , so A squared is equal to 2.5 | |
04:53 | squared . This is plus B squared , which is | |
04:56 | why squared this is equal to c squared 3.5 squared | |
05:01 | . So what does this equal ? Well , 2.5 | |
05:03 | times 2.5 . This is 6.25 plus y squared is | |
05:09 | equal to 3.5 times 3.53 point five times 3.5 is | |
05:13 | 12.25 So why squared is going to be equal to | |
05:19 | 12.25 ? Subtract 6.25 which is going to be six | |
05:25 | . Therefore why is going to be equal to the | |
05:28 | square root of six ? So we're almost done . | |
05:31 | The distance that we're trying to find out is equal | |
05:34 | to X plus Y . We have X here , | |
05:37 | which is two square root six and we have Y | |
05:39 | , which is the square root of six . So | |
05:41 | we add these guys together and we get our answer | |
05:44 | unknown distance here will be equal to three times the | |
05:47 | square root of six . Math . This is the | |
05:49 | exact answer here , but we can give an approximate | |
05:52 | by working at the square root of six , which | |
05:53 | is around about 2.45 are multiplying it by three . | |
05:57 | Our answer is around about 7.35 . Anyway , how | |
06:02 | did you go with that ? Did you like that | |
06:03 | problem ? If you did give us a thumbs up | |
06:06 | and put us in the comments about how you went | |
06:08 | with it , there are going to be more problems | |
06:13 | coming along and I thank you for watching . We'll | |
06:14 | see you next time . Bye . |
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