Question 1174336: A new flat screen TV is surrounded by a plastic border to protect the screen itself. The protective plastic border is uniform in width and has outer dimensions 36” by 40”. The actual screen is 80% of the total area of the flat screen TV. What is the width of the uniform plastic border and what are the dimensions of the actual screen?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A new flat screen TV is surrounded by a plastic border to protect the screen itself.
The protective plastic border is uniform in width and has outer dimensions 36” by 40”.
The actual screen is 80% of the total area of the flat screen TV.
What is the width of the uniform plastic border and what are the dimensions of the actual screen
:
let w = width of the border
then
(36-2w) = width of the TV screen
and
(40-2w) = the length
:
The equation
(36-2w)*(40-2w) = .80(36*40)
FOIL, do the math
1440 - 72w - 80w + 4w^2 = .8(1440)
1440 - 152w + 4w^2 = 1152
Arrange as a quadratic equation
4w^2 - 152w + 1440 - 1152 = 0
4w^2 - 152w + 288 = 0
Simplify, divide by 4
w^2 - 38w + 72 = 0
this will easily factor to
(w-2) = 0
and
(w-36) = 0
the reasonable solution
w = 2 inches is the width of the border
:
:
Check this, subtract 4 from each dimension
32 * 36 = 1152
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