(male narrator)
In this video, we will be looking at the area
of picture frames. To help us visualize
the frame, we will always want
to draw a picture. We want to remember
as we set up the problem, the frame is on the top
and bottom of the picture. It is also on the left
and right sides and must be considered
on both sides, not just one. So in this example,
which describes a picture… which measures
10 inches by 7 inches, is placed in a frame
of uniform width. We’re looking for the width
of the frame, which we
don’t know. Let’s call it x. This x is on both sides
of the picture, so when I want to describe the
top of the picture frame here, we have a 7, an x, and an x,
or a total of 7 plus 2x. Similarly, the frame is
on the top and bottom, so the height of the frame
becomes 10 plus 2x. We’re told
that the total area of the frame and picture
together is 208. If we multiply
width times length, this will give us
the area: 7 plus 2x, times 10, plus 2x,
is equal to the area of 208. We can start solving
this equation by multiplying it
using FOIL to get 70, plus 14x, plus 20x,
plus 4x squared, equals 208. Combining like terms and putting
things in order gives us: 4x squared, plus 34x,
plus 70, equals 208. In order to solve, we want
the equation to equal 0, so we will subtract 208
from both sides. This gives us 4x squared,
plus 34x, minus 138, equals 0. We can now start factoring
in order to solve it by factoring out the GCF of 2
to get 2x squared, plus 17x, plus 16…or minus 69…
equals 0. We can continue factoring…
this expression to get 2x, plus 23, times x,
minus 3, equals 0. If you could not find
those two factors, we could’ve used the quadratic
formula on this trinomial, using a as 2, b as 17,
and c as -69. Both will give us
the same final result. Once it’s factored, we set each factor equal to 0
that has a variable in it. Now, we can solve
the remaining equation by subtracting 23
to get 2x equals -23, and dividing by 2
to get x equals -23/2; or solving
the other equation by adding 3
to get x is equal to 3. Remember, x represents
the width of the frame. It would not have
a negative width to it, so we can throw
the negative number out. The only answer left
for the width of the frame is x equals 3, telling us our frame
has a width of 3 inches. In Part 2 of this video, we’ll
take a look at another example where we have
a frame and are asked to find
the width of the frame. As we set these problems up,
it is important to remember that the frame is
on the left and right sides, giving us 2x
in the top and bottom sides.

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1. omitobeats says:

THANK YOU! this video is just what I needed to learn before my math exam on tuesday. THANK YOUUUUUUUUUUUUUUUUUUUUUUUUU