 Now You can't solve this equation all three over one shot because an equation basically means you're only solving with one equal sign So what you can do is combine these two guys to solve for X and then combine this guy this guy To solve for W. So what you do is to solve this equation to solve for W and X What you would do is say okay Five over that five over ten is equal to six over W. Let's do this over here So what you're going to do is go five over ten is equal to six over W Now to get rid of fractions all you got to do is cross multiply So the bottom guy from over here comes to the top over here the bottom guy from over here comes to the top over here So this becomes five W is equal to ten times six to sixty and then divide by five divide by five So W is equal to sixty divided by five is twelve So right away You just solve for W which is over here, which is Now you want to solve for X. Oh, sorry you solve for W you solve for X Let's change this up So this is X. So you just solve for this guy, which is 12 Use the right symbols in the right places Now you want to solve for W All you do is combine this guy and this guy You could combine this and this because you already have you just solve for X you have this but to again Make sure you're not Continuously Continuing error from one question to the other just use the use the Numbers that they gave you instead of using numbers you calculated just in case you made a mistake here because if you use The 12 here and if you made a mistake to try to figure out what W is then the W is going to be wrong because this was wrong So go back to the original what they gave you and related to that. Okay, so this would be five over ten is equal to W over eight. So again what you do is cross multiply So this becomes eight times five is 40 is equal to 10 W And then divide by ten divide by ten. So W is equal to four So you just solve for W which is for so basically this is a Triangle that you had W is equal to W that way is equal to four So this becomes four. So what you had here was a triangle that's been Multiplied by two to give you these dimensions. So this guy is twice as big as this guy. It's simple as that you're doing Similar triangles you're using ratios to solve one triangle by knowing the dimensions of another triangle And all you need is a connector the connectors are all the angles have to be the same and you have to have The dimensions the length of the same side from both triangles and that for us was Five and ten that was a ratio that we we could use to solve the other and the other sides Okay, I'm going to do one more just to clear things up here So let's do one more similar triangle. We understand congruent triangles congruent It's just basically if they're identical triangles and all you need is side side side Side angle side or angle side angle, which is the same as angle angle side So for similar triangles what we need is angle angle angle So if they give you a triangle, let's say this guy and They give you another triangle. Let's say this guy And they say this guy is equal to this This is equal to this and that is Equal to that let's give this is a five Point one Let's make this one X. Let's just make this one two Let's make This guy the relationship make it 17.3 Give this one as Six and this one as Q So what you're going to try to do is say Connect up the sides with each other and put them as ratios Okay So one side which is equivalent to the other side in this in the other triangle the similar triangle on top of each other so what you're going to do is look at the angles and Connect up the sides. So this is a double-tick angle and that's a double-tick angle So this guy controls the opposite side and this guy controls the opposite side. So what you're going to do is say 5.1 over 17.3 must be equal to here's a triple side which is X over Six must be equal to here's a single side two over Q Now the one thing to keep in mind is if you call this triangle a and if you call this triangle b Then all the links for triangle a go up top and all the links for triangle b go in the bottom Do not switch these up Otherwise the answer is not going to be correct Now you can switch up the whole thing and put all the b's on top and put all the a's in the bottom But you have to be consistent if you're putting all the links For side a up top they all have to go up top if you start off with side b length in the bottom Then the rest of the sides for the b triangle has to go in the bottom for you to be able to solve this okay, so Now that we have this we can start solving for X and Q what you do is you do your cross multiplication Again, all you're doing is taking a chunk out of this and Leaving that one alone solving for X and then you're going to take this guy and this guy do the same thing solve for Q so 5.1 over 17.3 Must be equal to X over 6 So what you do now is to get rid of your fraction cross multiply what we got is 6 times 5.1 6 times 5.1 is 30.6 is equal to 17.3 X and what you do you've got to get X by itself Divide by 17.3 divide by 17.3. So 30.6 divided by 17.3 is 1.768 If you round it up 8 so X is 1.769 that's rounded up to three decimal places to solve for Q We got that now. I'm going to erase it if we're going to solve for Q What we're going to do is we're going to take 5.1 over 17.3 equals to 2 over Q 5.1 over 17.3 is equal to 2 over Q Again, what we're going to do cross multiply so Q comes up and multiplies this this guy comes up and multiplies that So that's going to be 5.1 Q is equal to 17.3 times 2 17.3 times 2 Which is 36.6 34.6 divided by 5.1 divided by 5.1 So Q is going to be equal to 34.6 divided by 5.1 is 6.78 6.78 So Q is going to be 6.7 So to be consistent if we took this to two decimal places, we want to express this to two decimal places So we're going to round 69 up to 7 What you should do now is do a visual confirmation to make sure you got everything correct. Let's see 5.1 is equivalent to 17.3 Across from the triple tick is 1.7177 and that's 6 And across from the single tick is 2 and across from the single tick is 6.78 So this guy is the smallest side here and This guy is the smallest side that makes sense. That's the middle side That's the middle side and that's the longest side and that's the longest side Okay, so visually you should confirm at the end if it makes sense the numbers might be a little off But if it works out like this you should have done it correctly. You should have the right answers, okay? So this is similar triangles and it's extremely useful when you're trying to find The dimensions of one triangle when you don't know the exact angles and it's not a right angle triangle Because that way if it's not a right angle triangle you can't use the Pythagorean theorem You have to use something else. So what you do is you do a comparison from one triangle to another triangle And that's similar triangles, okay? Good luck in the problems