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# Television Problem | AMC 10A, 2008 | Problem 14

Try this beautiful problem from Geometry:Squarefrom AMC-10A (2008) You may use sequential hints to solve the problem.

Try this beautiful Television Problem from AMC – 10A, 2008.

## Television Problem – AMC-10A, 2008- Problem 14

Older television screens have an aspect ratio of 4: 3 . That is, the ratio of the width to the height is 4: 3 . The aspect ratio of many movies is not $4: 3,$ so they are sometimes shown on a television screen by “letterboxing” – darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of 2: 1 and is shown on an older television screen with a 27 -inch diagonal. What is the height, in inches, of each darkened strip?

,

i

• $2$
• $2.25$
• $2.5$
• $2.7$
• $3$

### Key Concepts

Geometry

Square

Pythagoras

But try the problem first…

Answer: $2.7$

Source

AMC-10A (2008) Problem 14

Pre College Mathematics

## Try with Hints

First hint

The above diagram is a diagram of Television set whose aspect ratio of $4: 3$.Suppose a movie has an aspect ratio of $2: 1$ and is shown on an older television screen with a $27$-inch diagonal. Then we have to find the height, in inches, of each darkened strip.

we assume that the width and height of the screen be $4x$ and $3x$ respectively, and let the width and height of the movie be $2y$ and $y$ respectively. If we can find out the value of $x$ and $y$ then  the height of each strip can be calculate eassily

Can you now finish the problem ……….

Second Hint

By the Pythagorean Theorem, the diagonal is $\sqrt{(3 x)^{2}+(4 x)^{2}}=5 x=27 .$ So $x=\frac{27}{5}$

Now the movie and the screen have the same width, $2 y=4 x \Rightarrow y=2 x$

can you finish the problem……..

Final Step

Thus, the height of each strip is $\frac{3 x-y}{2}=\frac{3 x-2 x}{2}=\frac{x}{2}=\frac{27}{10}=2.7$

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