(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.

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