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# Manipulating formulas: area

Video transcript

The formula for the
area of a triangle is A is equal to 1/2 b times
h, where A is equal to area, b is equal to
length of the base, and h is equal to the
length of the height. So area is equal to
1/2 times the length of the base times the
length of the height. Solve this formula
for the height. So just to visualize
this a little bit, let me draw a triangle here. Let me draw a triangle just
so we know what b and h are. b would be the
length of the base. So this distance
right over here is b. And then this distance
right here is our height. That is the height
of the triangle-- let me do that at a lower
case h because that's how we wrote it in the formula. Now, they want us to solve
this formula for the height. So the formula is area is
equal to 1/2 base times height. And we want to solve for h. We essentially want
to isolate the h on one side of the equation. It's already on the
right-hand side. So let's get rid of everything
else on the right-hand side. So we can do it-- well, I'll
do it one step at a time. We could kind of skip
steps if we wanted to. But let's see if we can
get rid of this 1/2. So the best way to get
rid of a 1/2 that's being multiplied by
h is if we multiply both sides of the equation
by its reciprocal. If we multiply both sides of
the equation by 2/1 or by 2. So let's do that. So let's multiply--
remember anything you do to one side
of the equation, you also have to do to the
other side of the equation. Now, what did this do? Well, the whole point
behind multiplying by 2 is 2 times 1/2 is 1. So on the right-hand
side of the equation, we're just going to have a bh. And on the left-hand side of
the equation, we have a 2A. And we're almost there, we
have a b multiplying by an h. If we want to just
isolate the h, we could divide both sides
of this equation by b. We're just dividing both sides. You can almost view b as
the coefficient on the h. We're just dividing
both sides by b. And then what do we get? Well, the right-hand
side, the b's cancel out. On the left-hand side, we're
just left with 2A over b. So we get h-- and I'm just
swapping the sides here. h is equal to 2A over b. And we're done. We have solved this
formula for the height. And I guess this
could be useful. If someone just gave
you a bunch of areas and a bunch of base
lengths, and they said keep giving me the
height for those values, or for those triangles.