Question 1199115
Last question for today. 

The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in 4 : 3 format, meaning the ratio of the length to the width of the rectangular screen is 4 to 3. What is the area of a 37-inch Traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger? 

Hint given but the textbook:

If x is the length of a 4 : 3 format screen, then (3x/4)is the width.

Let me see.

I know what x represents. I will say let y = length of a 16 : 9 format screen. If this is true, then 9y/16 is the width. 

My set up for x goes like this: 

37 = x(3x/4)

Solving for x, I get 7.024.

My set up for y goes like this:

37 = y(9y/16)

Solving for x,I get 8.11035.

I see that y > x,meaning the LCD TV screen format is bigger. 
However, according to the textbook,I am wrong.

Textbook Answer:

The screen of a 37-inch TV in 4 : 3 format has an area of 657.12 in^2.
The screen of a 37-inch TV in 16 : 9 format has an area of 587.97 in^2.
According to the textbook, the traditional TV has the bigger screen.

Questions:

1. What did I do wrong?

2. What is the correct set up for each TV to find the area?

3.  I have a hard time setting up the correct equation(s) leading to the right answer for most word problems. How can I improve my word problem-Solving skills?.

Thanks 
<pre><font color = red><font size = 4><b><u>THE ERROR</font></font></b></u>
For the LCD, you have: {{{matrix(1,3, 37, "=", y(9y/16))}}}, but it should be: {{{matrix(1,3, (16y)^2 + (9y)^2, "=", 37^2)}}}, which gives you: {{{matrix(4,3, 256y^2 + 81y^2, "=", "1,369", 337y^2, "=", "1,369", y^2, "=", "1,369"/337, y, "=", sqrt("1,369"/337))}}}
                                                                                y = 2.01551843 = 2.02 inches (ROUNDED)

16:9 = 16(2.02):9(2.02) = 32.32 by 18.18 (Dimensions)
Area of LCD TV: 32.2(18.18) = 587.5776, or 587.58 in<sup>2</sup>.

Using the same concept, find the area of the traditional TV (should be close to the book's answer). Then, compare the areas of the 2.</pre>