A television screen is 40 cm high and 60 cm wide. The picture is compressed to 62.5 % of its original area, leaving a uniform dark strip around the outside. What are the dimensions of the reduced picture?

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- Sep 22nd 2008, 05:13 PM #1

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Hello, Andrew!

A television screen is 40 cm high and 60 cm wide.

The picture is compressed to 62.5 % of its original area,

leaving a uniform dark strip around the outside.

What are the dimensions of the reduced picture?Code:: - - - 60 - - - - : - *-------------------* - : | | x : | *-----------* | - : | | | | : 40 | | | | 40-2x : | | | | : : | *-----------* | - : | | x - *-------------------* - : x : 60-2x : x :

The area of the picture is: .$\displaystyle (40-2x)(60-2x) \:=\:4x^2 - 200x + 2400$ cm².

The area of the picture is $\displaystyle \frac{5}{8}$ the area of the screen:

. . $\displaystyle 4x^2 - 200x + 2400 \:=\:\frac{5}{8}(2400) \;=\;1500 \quad\Rightarrow\quad 4x^2 - 200x + 900 \:=\:0$

Factor: .$\displaystyle 4(x-5)(x-45) \:=\:0 \quad\Rightarrow\quad x \;=\;5,\:45$

The dark strip is 5 cm wide.

Therefore, the dimensions of the picture are: .$\displaystyle 30\text{ cm } \times 50\text{ cm.}$

*You're absolutely correct, Lucky!*

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