1. ## 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?

2. Would it not be 30cm by 50cm?

3. 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?
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!