If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:2:09

- [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.