### Video Transcript

The area of a triangle is 12𝑥
squared plus four 𝑥 square centimeters, and its base is four 𝑥 centimeters. Write an expression for its
height.

Let’s begin by recalling how we
find the area of a triangle. For a triangle whose base is 𝑏
units and whose perpendicular height is ℎ units, its area is a half base times
height. And the area will be given in
square units. Now, it doesn’t matter that we’re
working with algebraic expressions. We can still substitute these into
this formula.

Let’s let the height be equal to ℎ
or ℎ centimeters. We’re told the area is 12𝑥 squared
plus four 𝑥 and its base is four 𝑥. So we can write 12𝑥 squared plus
four 𝑥 equals a half times four 𝑥 times ℎ. Now, because we can find a half of
four 𝑥 quite easily, we should. This will make the next step a
little bit easier. But if we couldn’t, what we could
do is multiply both sides by two.

We’re not going to do that
though. We’re going to write the right-hand
side as two 𝑥 times ℎ. And then since we’re looking to
find the value of ℎ or certainly an expression for ℎ, we solve for ℎ by dividing
through by two 𝑥. So ℎ is 12𝑥 squared plus four 𝑥
all over two 𝑥.

There are a number of ways we can
simplify this fraction or divide the numerator by the denominator. One way is to use the bus stop
method. So let’s see what that looks
like. Since we’re dividing by a monomial,
we don’t need to use long division. We’re simply going to divide each
term in our dividend, that’s the quadratic here, by the divisor, that’s two 𝑥. So 12 divided by two is six, and 𝑥
squared divided by 𝑥 is 𝑥. So we see that 12𝑥 squared divided
by two 𝑥 is six 𝑥. Then we divide four 𝑥 by two
𝑥. Well, four divided by two is two,
and 𝑥 divided by 𝑥 is one. So when we divide 12𝑥 squared plus
four 𝑥 by two 𝑥, we get six 𝑥 plus two. And so that’s our expression for
ℎ.

It is, of course, worth noting that
we’re working in centimeters and square centimeters. So the units for the height ℎ are
in centimeters also. The height is six 𝑥 plus two
centimeters.