 This video is solving problems using proportional parts number three So first off we need to solve for x and it's kind of strange since we've got a full side length 3x minus 2 Well, that shouldn't be too big a problem because we've got 3 and 5 So we can compare proportional parts by adding 3 and 5 together And so then we'll just cross multiply to solve so we get x equals 6 Now, let's take a look at one more problem. So here we have segment er is the mid segment of this triangle Now remember mid segment means three things for us One thing it means is that Point e is the midpoint of segment nh And so that means these segments are congruent And likewise point r is the mid point of ny So these lengths are congruent as well A couple of the things the mid segment is parallel To its opposite side And also it creates a couple of pairs of congruent angles This angle is congruent to this angle Because they're corresponding angles cut by a transversal of parallel lines and then also this angle Is congruent to that angle Now the problem asks us to solve for x So x refers to side lengths In particular side lengths nr And ry Now because er is a mid segment I know that those side lengths must be equal And so we have a couple of terms with an x squared We have a term with a regular old x and we have a term with a constant number So it looks like we're going to have to do some solve by factoring So let's go through a cleanup session Let's bring that x squared to x squared over to the other side by subtracting 2x squared from both sides And then again since we want to solve by factoring we'll have to do the same with 7x And so now we're looking for factors of 12 which add to negative 7 All factors of 12 it's either 2 and 6 Or 3 and 4 so negative 3 and 4 will do the trick if x minus 3 Times the quantity x minus 4 equals 0 So now either the first term is equal to 0 or the second term is equal to 0 So if x minus 3 is equal to 0 That means x could possibly be positive 3 If x minus 4 equals 0 That means x could be equal positive 4 So now we have two potential answers Let's just go through and make sure that the side lengths make sense geometrically as well as as pardon me Geometrically as well as algebraically So I'll take this value of x maybe I'll try x equals 3 first And I'll substitute it in for the values of 3x squared plus 12 and 2x squared plus 7x Both of those end up being 39 So I know that x minus 3 is a possible answer Let's check x equals 4 as well both of those Make that length 60 Now since both of these sides are positive It is possible that x is both either 3 or 4 So we have two answers in this case 3 or 4 Thanks for watching