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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.

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

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.
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

Last edited by x2suresh on 04 Sep 2008, 11:06, edited 1 time in total.

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

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?

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
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

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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