00:01
So using what we know about similarity, we can solve for x.
00:08
And so let's start with a.
00:11
In a, we can see we have these little squares here.
00:16
And what that means is all these angles are the same.
00:24
So you have this rectangle here.
00:28
The longer side is six here and the longer side is x here.
00:31
So we can say that these are congruent in the longer, or the shorter side here and here are similar.
00:39
So we can write this as 2 is equal to 4 over 6 is equal to x.
00:50
And now we solve.
00:52
The way we solve is by cross multiplying like this.
00:56
The 2 is multiplied by the x and the 6 is multiplied by the 4.
01:02
What does that give us? that gives us 2x is equal to 6 times 4.
01:08
That's 24.
01:09
And now we solve for x by dividing 2 on both sides.
01:14
So for a our x is equal to.
01:20
So now let's move on to b.
01:24
As we see here, this angle and this angle are similar, which means that or also this angle and this angle are similar and similar to these two which means this side and this side are similar.
01:50
So we can write this as x minus 5 is equal to 6 and also the 3 is opposite from the 6 and the 4 is opposite from the x minus 5 so those two are similar.
02:06
So underneath the x minus 5 you want to write this four because the four is in that same shape and underneath the six you want to write three the same numbers go with the same shapes here and again we cross multiply so that's equal to x five times three so we'll write three x minus five is equal to four times six so now we distribute the three to the x so that gives us three x minus 3 times that 5 plus 15 is equal to 24 now we solve for x by adding 15 on both sides let's make some room here so 24 plus 15 so that is 39 this cancels out 3x is equal to 39 divide by 3 on both sides divide by 3 on both sides so our x is equal to 13 and that is our answer for b.
03:23
Now let's move on to c.
03:28
So for c, these again, these boxes mean that all of these are the same angle.
03:43
And this x is similar to this 21.
03:50
Okay? and for this one here, we know, that the perimeter is 60, but what we don't know are the other sides here...