- [Instructor] In this problem,
we have a rectangle
that has a length that is three more
than triple the width.
We want to find the
dimensions of such a rectangle
if the area's gonna be 36 inches squared.
So the first thing we want to do
is we want to think about
what is area of a rectangle?
Well area of a rectangle
is equal to length times the width.
Now they gave us enough information
to find a relationship between
the length and the width.
In fact, they told us that the length
is three more than triple the width.
So as an equation,
length is equal to triple the width,
and then three more, so plus three.
Now what we're gonna do
is we're gonna take that L
and substitute it into
our equation for area,
to get it all in terms of one variable.
So we got 3W plus 3
times W is A.
This is actually a quadratic,
because if I distribute the W,
I get 3W squared plus 3W,
and there's my quadratic function.
Now we're looking for one specific one.
We're looking for one
that has an area of 36 inches.
So we're gonna be putting
that in for the output here.
So over here I'm gonna set
36 equal to my quadratic,
3W squared plus 3W,
and now some common things
that I see at this point.
You might, people sometimes
try to subtract the 3W
and take the square root.
We can't do that.
Anytime you got a W squared term,
and a W term,
what we're gonna need to do
is get a quadratic equal to zero,
and then either factor,
or use the quadratic formula,
or use our graphing calculator.
So let's see what happens.
What we'll do is we'll
get it equal to zero,
so subtract 36 from both sides.
So those cancel.
So we have zero equals
3W squared plus 3W minus 36.
Let's try factoring first,
but you don't have to spend
a lot of time on factoring,
because we have a quadratic equal to zero,
if this didn't factor,
go right to the quadratic formula,
or if you're not sure if it factors,
go right to the quadratic formula.
Now one thing I noticed
is all of them have a term of three in it.
So I pull out a three,
and I get W squared
plus W minus 12.
This makes it a little easier
to recognize that it's gonna factor.
Because I'm gonna be able to
split it into two factors,
with W being the first term.
The reason I notice it's gonna factor
is I need to end up
with a W in the middle,
so I need two factors of
12 that are one apart.
Well, three and four.
The only last thing is I
need it to be a positive W,
so I'm gonna add four and subtract three.
I know my signs will be opposite
because of the negative 12.
So these are just some
things we can look for.
So we get W equals three from this one,
and from here we get W
equals negative four.
Now it doesn't make any sense
to have a negative width,
so we're gonna get rid of that answer,
and W equals three is part of our answer.
Now we also have to go back and find L.
Remember, we already have a relationship
between L and W that we found earlier.
So the length is equal to
three times the width we found
plus another three, or nine,
so the dimensions of this
rectangle are nine inches
by three inches,
and that's how we can use a quadratic
to solve this problem.
