- [Voiceover] The length of a
rectangle is three inches more
than its width.
Its area is 130 square inches.
Find the width and the
length of the rectangle.
So using this rectangle here,
because the length is the longer side,
it is three inches more than the width,
we'll let the width be equal to x.
And therefore the length would
be equal to x plus three.
We also know the area is
equal to 130 square inches.
And now using the area
formula for a rectangle,
we can set up an equation and solve for x,
then determine the length and the width.
The Area of a Rectangle is
equal to length times width.
So we'll substitute 130 for the area.
And for the length times
the width we'd have
the quantity x plus three,
times x.
Or if we want we could write this as
x times the quantity x plus three.
Let's go ahead and change the
order of this multiplication.
So 130 equals x times the
quantity x plus three.
Now we want to solve this equation for x.
So let's clear the parentheses
by distributing here.
So 130 is equal to x squared plus three x.
Because we have a quadratic equation,
let's set it equal to zero
and see if we can solve by factoring.
So we'll subtract 130 on both sides.
130 minus 130 is zero,
so we have zero equals x squared,
plus three x,
minus 130.
And now if this does factor,
it'll factor into two binomial factors.
Because the first term is x squared,
and x times x equals x squared,
we'll have a factor of x here and here,
in the first positions
of the binomial factors.
Because the leading coefficient is one,
the terms in the second
positions would be the factors
of negative 130, that
add to positive three.
And because 10 times 13 equals 130,
and we're looking for two factors
that give us a product of negative 130,
and add to positive three,
we can use the factors
of positive 13 and negative 10.
So for positive 13, we write plus 13 here.
For negative 10, we write minus 10 here.
Again, 13 times negative
10 equals negative 130.
And 13 plus negative 10
equals positive three.
So this is now factored,
and because this product is equal to zero,
x plus 13 must be zero,
or x minus 10 must equal zero.
Solving for x here, we
subtract 13 on both sides,
x equals negative 13.
Or, solving for x here,
we add 10 to both sides,
x equals positive 10.
Remember, x and x plus
three represent a length,
which must be positive.
So even though x equals negative
13 is an algebraic solution
to our equation,
it's not a solution to
this application problem.
So we can eliminate x equals negative 13.
And our solution is x equals 10.
So if x equals 10, and the
length is x plus three,
the length would be 10 plus
three, which equals 13.
So this length is 13 inches.
We don't include the
units here in our answer.
We just enter 13.
And the width is x, and
we know x equals 10,
so the width is 10 inches, so we enter 10.
The area of a 10 by 13 rectangle,
would be 10 times 13, which
equals 130 square inches.
And notice how with these dimensions,
the length is three inches
more than the width.
I hope you found this helpful.
