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 . |
Summarizer
DESCRIPTION:
OVERVIEW:
How to solve this viral math problem is a free educational video by tecmath.
This page not only allows students and teachers view How to solve this viral math problem videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.
GRADES:
STANDARDS:
