From OG: If TV screens were flat, the area of a 21-inch

Question

From OG:

If TV screens were flat, the area of a 21-inch screen would be how much bigger than the area of a 19 inch.


I have the answer below - math too complicated, answer too simple. Gimme an easier way if you have one.

Thanks

Caspace · Answer

From OG:

2x^2 = 19^2 => 361/2 = 180.5

2x^2 = 21^2 => 441/2 = 220.5

Answer is 40.


Seems too simple an answer with so much ugly math. How can i find a faster way.

hornsfan2005 · Answer

I'm not sure I really understand the problem. Are we supposed to assume the screen is rectangular? Also, how did you get those equations?

Rupstar · Answer

Where does 2x^2 come from???
if TV's are said to be 19 inches it means it is 19 by 19
19*19= area1
21*21=area2
441-361=80
I dont get what this divisor of 2 is for
where in OG is this?

hornsfan2005 · Answer

same question i had....i don't understand the 2x divisor part.

Caspace · Answer

Iti s OG #245 - i may have missed a little of the needed details so let me check.

They are square. So we use a isoceles approach with the 2x's as in 


x:x:x2^1/2 triangle.

Caspace · Answer

Some how i got some "emoticons" on my last post.

they explanation has x^2 + x^2= 19^2 and x^2 + x^2= 21^2 

I left out the all important square part.

hornsfan2005 · Answer

If it is square, then your approach is correct, cap space. you'll have to solve for the sides of the square.

for the 19'' - each side is 19/sqrt 2 
for the 21'' - each side is 21/sqrt 2

square both sides and take the difference, as you did.

Caspace · Answer

can you think of a faster method though i hate the thought of squaring and dividing such unruly numbers on the test.

hornsfan2005 · Answer

not sure caspace.... i think the calculations could be done under 2 minutes though. usually whenever i see problem with diagonals, my first instinct is to think of a square/geometry. 

P.S. I apologize for messing up your name in my last post!

Caspace · Answer

thanks for the help. i suppose you are right. i was just thinking with the final answer at 40 there had to be trick in there somehow.

I will post if i think of something.

Rupstar · Answer

OK lemme redo the question guys:
FROM OG:

The size of a TV screen is given as the length of its diagonal. If screens were flat, then the area of a 21 inch screen is how many sq inches greater than the area of a 19 inch.

the explanation is pretty simple and not hard
they also tell you it is square...so no flat screen wide view TV or anything to consider.

19inch TV:
x^2+x^2=19^2
2x^2=19^2
X^2=?

Same for the 21 inch tv...just some math and geometry rules...i dont think there can be any other way
Answer:220.5 -180.5

Caspace · Answer

my real issue was a short cut any thoughts on that. i saw this kind of a problem as a potential time loser w/o a trick and time saver with a trick.

batliwala · Answer

usually sceen size is length of diagonal. Since the screen is a square the formula given holds good.

700Plus · Answer

Interesting. I dont see in the math explanation that the TV is a square.In reality they are not.They are 4:3( regular ones,not taking wide tv's into consideration).I hope, actual problem descriptiobn has the right info, else It is not inconsistent( to expect screen size is measured by its diagnal at the sametime screen is of square shape).

From OG: If TV screens were flat, the area of a 21-inch

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