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# What is the ratio of the area of the TV screen with diagonal

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Current Student
Joined: 11 May 2008
Posts: 551
What is the ratio of the area of the TV screen with diagonal [#permalink]

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04 Sep 2008, 02:24
What is the ratio of the area of the TV screen with diagonal 18'' to that of the screen with diagonal 15''?

1. The ratio of width to length is the same for both screens
2. The width of the 18''-screen is 20% greater than that of the 15''-screen

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Director
Joined: 14 Aug 2007
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04 Sep 2008, 03:03
arjtryarjtry wrote:
What is the ratio of the area of the TV screen with diagonal 18'' to that of the screen with diagonal 15''?

1. The ratio of width to length is the same for both screens
2. The width of the 18''-screen is 20% greater than that of the 15''-screen

we have to find out, l1w1/l2w2

1 tells us that $$w1/l1 = w2/l2$$ i.e $$w1/w2 = l1/l2$$ i.e the widths and lengths of the rectangles are proportional. Thus these two form similar rectangles. and though units may be different we can find out the ratio w1l1/w2l2

2 tells us that w1=1.2w2 i.e w1/w2 = 1.2, also given is that d1/d2=18/15 = 1.2, thus width and rectangles are in proportion. so again these two are similar triangles and ratio can be found.

D for me.. please post OA when correct.
Current Student
Joined: 11 May 2008
Posts: 551

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04 Sep 2008, 05:27
can someone fill me in more on similar rectangles. had heard of similar triangles.
when can we say that two rectangles are similar?
and conversely if two rectangle are similar , what can we infer

the OA IS d.
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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Updated on: 04 Sep 2008, 11:06
alpha_plus_gamma wrote:
arjtryarjtry wrote:
What is the ratio of the area of the TV screen with diagonal 18'' to that of the screen with diagonal 15''?

1. The ratio of width to length is the same for both screens
2. The width of the 18''-screen is 20% greater than that of the 15''-screen

we have to find out, l1w1/l2w2

1 tells us that $$w1/l1 = w2/l2$$ i.e $$w1/w2 = l1/l2$$ i.e the widths and lengths of the rectangles are proportional. Thus these two form similar rectangles. and though units may be different we can find out the ratio w1l1/w2l2

2 tells us that w1=1.2w2 i.e w1/w2 = 1.2, also given is that d1/d2=18/15 = 1.2, thus width and rectangles are in proportion. so again these two are similar triangles and ratio can be found.

D for me.. please post OA when correct.

good catch on 2nd statement.

I almost missed that.
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Originally posted by x2suresh on 04 Sep 2008, 08:18.
Last edited by x2suresh on 04 Sep 2008, 11:06, edited 1 time in total.
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Joined: 05 Jul 2008
Posts: 1340

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04 Sep 2008, 09:34
Can some one explain it more clearly?

Given is l1^2 + w1^2 =18 ^2 & l2^2 + w2^2 =16 ^2

Find l1w1/l2w2

1) says l1/w1=l2/w2

Total 4 unknowns (l1, w1 and l2, w2) 3 equations How can we solve for l1w1/l2w2?

2) w1= 1.2 w2

Total 4 unknowns (l1, w1 and l2, w2) 3 equations How can we solve for l1w1/l2w2?

Combine them, we can solve 4 equations 4 unknowns

How ever I am wrong as the OP says the answer is indeed D.
Retired Moderator
Joined: 18 Jul 2008
Posts: 904

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04 Sep 2008, 10:00
I have the same question as icandy. They are asking for a specific value, not Yes/No question...

icandy wrote:
Can some one explain it more clearly?

Given is l1^2 + w1^2 =18 ^2 & l2^2 + w2^2 =16 ^2

Find l1w1/l2w2

1) says l1/w1=l2/w2

Total 4 unknowns (l1, w1 and l2, w2) 3 equations How can we solve for l1w1/l2w2?

2) w1= 1.2 w2

Total 4 unknowns (l1, w1 and l2, w2) 3 equations How can we solve for l1w1/l2w2?

Combine them, we can solve 4 equations 4 unknowns

How ever I am wrong as the OP says the answer is indeed D.
Intern
Joined: 03 Sep 2008
Posts: 22

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04 Sep 2008, 13:26
Hmmm. I'm getting that statement 1 is sufficient but statement 2 is not sufficient.

Before I go into my reasoning let me note that just because two objects are similar isn't enough to conclude that the ratio of the areas can be determined. Think of squares of different sizes. They satisfy statement 1 but we don't know the ratio of the areas unless we have more information. That's what the diagonals give us. If you don't use the diagonal measures in your reasoning then your reasoning is faulty.

Statement 1

We want to calculate l1w1/l2w2.

By statement 1 there exists k such that

l1/w1=l2/w2=k

==> l1=kw1 and l2 = kw2 .............(*)

==> l1w1/l2w2 = w1^2/w2^2

Now use the diagonal info, the pythagorean theorem and statement (*) to show

w1^2/w2^2=15^2/18^2

Statement 2

Let w1 = 5. Then w2=6

Use the Pythagorean theorem to find l1 and l2.

Calculate the ratio of the areas

Now do the same thing with w1=10 and w2=12

I get different ratios. So not sufficient.

Anyone else?
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Joined: 05 Jul 2008
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04 Sep 2008, 15:25
lsmv479 wrote:
Hmmm. I'm getting that statement 1 is sufficient but statement 2 is not sufficient.

Before I go into my reasoning let me note that just because two objects are similar isn't enough to conclude that the ratio of the areas can be determined. Think of squares of different sizes. They satisfy statement 1 but we don't know the ratio of the areas unless we have more information. That's what the diagonals give us. If you don't use the diagonal measures in your reasoning then your reasoning is faulty.

Statement 1

We want to calculate l1w1/l2w2.

By statement 1 there exists k such that

l1/w1=l2/w2=k

==> l1=kw1 and l2 = kw2 .............(*)

==> l1w1/l2w2 = w1^2/w2^2

Now use the diagonal info, the pythagorean theorem and statement (*) to show

w1^2/w2^2=15^2/18^2

I am with you until the Non red part. The diagonals d1 and d2 are 18 and 15 Not w1 and w2.

How can we just equate w1^2/w2^2 ( equivalent of ratio of areas ) to d1^2 /d2^2?

Am I missing anything obvious??
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Posts: 1738
Location: New York

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04 Sep 2008, 20:46
For Statement 2:

w1/w2=1.2
d1/d2 = 18/15=1.2

triangle formed by the sides l1 w1 d1 is right angle traingle.
triangle formed by the sides l2 w2 d2 is right angle traingle
and also ratio sides w1/w2=d1/d2 -- this is possible only if they are similar triangle.

so w1/w2=d1/d2=l1/l2

if you feel this is not true..please prove it..

area ratio = $$w1*l1/w2*l2 = w1^2/w2^2 = {1.2}^2$$

Statement 2 is suffcient
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Manager
Joined: 03 Jun 2008
Posts: 128
Schools: ISB, Tuck, Michigan (Ross), Darden, MBS

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07 Sep 2008, 00:35
x2suresh wrote:
For Statement 2:

w1/w2=1.2
d1/d2 = 18/15=1.2

triangle formed by the sides l1 w1 d1 is right angle traingle.
triangle formed by the sides l2 w2 d2 is right angle traingle
and also ratio sides w1/w2=d1/d2 -- this is possible only if they are similar triangle.

so w1/w2=d1/d2=l1/l2

if you feel this is not true..please prove it..

area ratio = $$w1*l1/w2*l2 = w1^2/w2^2 = {1.2}^2$$

Statement 2 is suffcient

Makes sense, super thx.

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Re: TV SCREEN   [#permalink] 07 Sep 2008, 00:35
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# What is the ratio of the area of the TV screen with diagonal

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