Math problem #6 - It doesn't look very hard...but can you do it? - Free Educational videos for Students in K-12

Math problem #6 - It doesn't look very hard...but can you do it? - By tecmath

Transcript


00:0-1	Good day and welcome the tech mouth channel . My
00:01	name is josh . We have a little problem here
00:03	today where we have a rectangle that has two intersecting
00:06	lines drawn through it , which breaks the rectangle up
00:08	into four different parts here . This part has an
00:11	area of one . This part has an area of
00:13	three . This part has an area of four .
00:16	Your job is to find the unknown area here .
00:19	So pause this video . If you'd like to give
00:20	this problem and try and when you're ready to keep
00:22	watching and learn how to solve this problem , started
00:25	up again . Mhm . Mhm . Time's up .
00:39	Did you manage to solve it ? There are a
00:40	number of different ways to solve this particular problem ,
00:42	but I'm going to choose what I think is the
00:44	simplest and fastest way . If you use a different
00:46	way , please put it in the comments below and
00:48	share it . So to start off , let's have
00:50	a look at these two triangle party , the one
00:52	with the area of four and the one with the
00:54	area of one . It's apparent that these two triangles
00:57	are similar to each other . That is they are
00:59	the same shape but they are different sizes and we
01:02	know this because we can work out the angles of
01:05	these . First off where we have these two lines
01:08	intersect to , we have vertically opposite angles which are
01:11	the same . We also have angles which are formed
01:14	by a line running through parallel lines which form alternate
01:18	interior angles . So these two angles are also the
01:21	same . In addition we also have this line which
01:24	runs through these two parallel lines here of our triangles
01:27	forming to interior angles that are also complementary to one
01:31	another . So as you can see this angle matches
01:33	up with this angle . This angle matches up with
01:35	this angle . This angle matches up with this angle
01:38	and what we're left with is too similar triangles .
01:41	So now what we can do is we can compare
01:43	the areas of these two triangles . These areas are
01:47	in proportion of one another . They are in a
01:48	4-1 ratio . What this means is something pretty special
01:52	. What it means is that the sides have a
01:55	ratio of two is to one because area is proportional
01:59	to side length squared and I'll tell you what I
02:01	mean by that even we don't have a triangle .
02:03	And that triangle was to have a side length of
02:05	six and this one must have a side length of
02:07	four . We could easily work out the area by
02:09	going length by width divided by 26 times four ,
02:12	which is 24 divided by two , Which is equal
02:15	to 12 . Now lives to have our sidelines would
02:18	have three and two . We could work out the
02:20	area of our little triangle here , three times two
02:24	is six , divided by two is equal to three
02:26	. You can see that are areas of a 4-1
02:28	ratio , but our side lengths have a 2-1 ratio
02:32	. So we can use this now to solve our
02:34	problem . If we call the height of this triangle
02:37	here , h it makes the height of the bigger
02:39	triangle to hatch . And so I can actually break
02:42	this up now into two rectangles . We have a
02:45	rectangle here , and we also have a smaller rectangle
02:49	up the top here . What's the area of our
02:52	larger rectangle ? Well , we know that half the
02:54	area is for because it's the triangle here . So
02:57	the entire area of this rectangle down here is going
02:59	to be twice as much which is going to be
03:01	eight for the smaller rectangle . Up here , we
03:03	know it's area is going to be for because it
03:06	has a height , that's half of this one here
03:08	, but the same length . So simply now ,
03:10	what we can do to work out the area of
03:11	our original rectangle where you can just add these two
03:14	together for plus eight . We have an area of
03:17	12 To solve our unknown area here , we simply
03:21	now take away are different sizes here -1 -3 -4
03:27	. And it leaves us with our answer 12 -1
03:31	-3 -4 is equal to four units squared . And
03:35	that is our answer . How did you go with
03:37	that ? Did you work it out without any help
03:39	? If you do let me know in the comments
03:41	and if you like that problem , please give us
03:42	a thumbs up anyway . Thank you for watching and
03:45	we'll see you next time . Bye .

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Math problem #6 - It doesn't look very hard...but can you do it? is a free educational video by tecmath.

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