# TV

• Sep 22nd 2008, 05:13 PM
andrewpark2
TV
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?
• Sep 23rd 2008, 08:21 AM
luckyc1423
Would it not be 30cm by 50cm?
• Sep 23rd 2008, 10:29 AM
Soroban
Hello, Andrew!

Quote:

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?

Let $\displaystyle x$ = width of the dark strip.
Code:

      : - - -  60 - - - - :     - *-------------------* -     : |                  | x     : |  *-----------*  | -     : |  |          |  | :   40 |  |          |  | 40-2x     : |  |          |  | :     : |  *-----------*  | -     : |                  | x     - *-------------------* -       : x :  60-2x  : x :
The area of the screen is: .$\displaystyle 40 \times 60 \:=\:2400$ cm².

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!