 So this video is solving problems using proportional parts number one. In order to solve this we need to set up proportions and the fact that we have these parallel lines within a triangle tells us we can use proportional parts of a triangle. So three and eight follow the same proportion as x plus two does to twelve. So let's set up our ratios. So now our job is to cross multiply. Three times twelve is equal to eight times the quantity x plus two. Three times twelve is thirty six and then eight times the quantity x plus two. Make sure we use the distributive property. And now we'll subtract ninety six from both sides of the equation. Wait a minute. Ninety six. That's incorrect. Eight times two is sixteen. If we subtract sixteen from both sides then we get eight x is equal to twenty. Dividing by eight on both sides gives you that x is equal to twenty-eighths which both are divisible by four. And so we get five over two is our value of x. Let's take a look at another example. So here we have two variables to solve. Let's deal with variable A first. Since A refers to the entire side length of that triangle we want to figure out the other side length in order to set up our ratios. So ten came from six plus four. So now we have our ratios. We have seven and eight follow the same ratio as four to ten. When you cross multiply we have four times A is equal to seven times ten. And seven times ten of course is seventy. And then we'll divide both sides by four. And that reduces to the fraction A is thirty-five halves. So there's A. Now our job is to also find B. So if we think about this figure as two overlapping triangles. This side the longer side that actually drew blue. I think color coordination would say it should be red. So eight corresponds with B. In the same way that let's say seven corresponds with thirty-five over two. Or maybe an easier one would be eight divided by B equals four divided by ten. So let's set up that ratio. So once again we have four divided by ten is equal to eight divided by B. And then we'll cross multiply. We have four B is equal to eight times ten which is eighty. And then divide by four on both sides. And now we get B is equal to twenty.