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Worked example: finding missing monomial side in area model
- [Voiceover] So we have a rectangle right over here. Let's say that we know that its area is 42x times y to the third. So that is the area of the rectangle. And we also know that the height right over here is 14xy and what we want to do in this video is figure out what the length is going to be. And as you can imagine, it's going to be in algebraic terms. So I encourage you to pause the video and figure out what is the length going to be if this height is 14xy and the area is 42xy to the third. Well, how do you figure out area? You take your length, and I'll just use L for length. I'll put L in parentheses. So you take your length and you multiply it times your height. So let's multiply it times 14xy and that's going to give you your area. So that's going to give us our area of 42xy to the third power. So how do we solve for our length? Well, we can just divide both sides by 14xy. So let's do that. So, let's divide the left-hand side and the right-hand side by 14xy, 14xy. Now on the left-hand side, I'm multiplying by 14xy and dividing by 14xy, that's the same thing as just multiplying or dividing by one so that cancels out. So I'm just left with L or our length which is the whole point of dividing both sides by 14xy. And on the right-hand side, I can look at the coefficients first. I could say 42 divided by 14, and that's going to be three. Three, and then I could say well, x divided by x that's just going to be one, and then I have y to the third divided by y. y to the third divided by y, that is going to be y to the third divided by y is going to be y-squared. And then we're done. Our length is three y-squared. So our length is equal to three y-squared.