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
Found 3 solutions by ikleyn, MathTherapy, math_tutor2020:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
In this my post, I will answer only the LAST your question: how to improve your skills solving word problems.
Go to web-page
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
It is the front page of the textbook Algebra-I, which I prepared at this forum for common use,
for everybody to learn from.
The right half of this page is for word problems.
So, click on every relevant link and go in depth, step by step and click by click, until you get real problems on the subject/topic you want.
Read and learn from there.
///////////////////
There are three ways to learn Math:
(a) Learn from good teachers;
(b) Read from good sources;
(c) Solve problems from good problem books.
Each of these listed ways is good, but they are even better in combinations.
I mean: in any combination.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! 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
THE ERROR
For the LCD, you have:  , but it should be:  , which gives you: 
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 in2.
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.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
We'll focus on the 4:3 tv for now.
x = length
3x/4 = width
When you wrote
37 = x(3x/4)
you are implying that the area is 37 square inches since
area = length*width
But the 37 inches refers to the length of the diagonal, and not the area.
We'll need the pythagorean theorem to tie together the length of each side, along with the diagonals.
Notice how drawing one diagonal splits the rectangle into two congruent right triangles.
This is why we're able to use the pythagorean theorem.
a = x = one leg
b = 3x/4 = the other leg
c = 37 = hypotenuse
The equation to solve is
a^2 + b^2 = c^2
x^2 + (3x/4)^2 = 37^2
I'll skip the steps. You should arrive at this solution
x = 148/5 = 29.6
We only focus on the positive x solution.
This decimal value is exact.
Use that x value to find 3x/4
3x/4 = 3*29.6/4 = 22.2
This decimal value is exact.
Therefore,
area = length*width
area = 22.2*29.6
area = 657.12 square inches
This area value is exact.
=====================================================
For the 16:9 tv, we'll solve this equation
a^2+b^2 = c^2
y^2 + (9y/16)^2 = 37^2
You should get this approximate positive y value
y = 32.248295
So,
9y/16 = 9*32.248295/16 = 18.139666
This value is approximate.
Then we can compute the following:
area = length*width
area = 32.248295*18.139666
area = 584.973300
area = 584.97 square inches
This area value is approximate.
=====================================================
One tip that could help with problem solving skills is to draw things out as much as possible.
In this problem, it's recommended to draw out each rectangle.
Then split those rectangles along one diagonal to produce the right triangles mentioned.
Another tip is to imagine you are trying to explain to somehow who isn't taking math.
This explanation process might help you translate concepts that were previously unfamiliar.
A third tip is to keep practicing. Math is a language.
The main way to get better at it is to keep trying to speak the language.
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