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# M10-05

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Intern
Joined: 12 May 2017
Posts: 8

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27 Dec 2017, 13:49
1
Bunuel wrote:
What is the ratio of the area of a rectangular TV screen with a diagonal of 18'' to that of a rectangular screen with a diagonal of 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.

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 51121

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27 Dec 2017, 20:40
1
Deepshikha1907 wrote:
Bunuel wrote:
What is the ratio of the area of a rectangular TV screen with a diagonal of 18'' to that of a rectangular screen with a diagonal of 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.

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.

You can find the area with diagonal^2/2 ONLY for squares. Yes, the diagonals of a rectangle are equal, but rectangles with equal diagonals have different areas.
_________________
Intern
Joined: 12 May 2017
Posts: 8

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27 Dec 2017, 23:42
Bunuel wrote:
Deepshikha1907 wrote:
Bunuel wrote:
What is the ratio of the area of a rectangular TV screen with a diagonal of 18'' to that of a rectangular screen with a diagonal of 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.

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.

You can find the area with diagonal^2/2 ONLY for squares. Yes, the diagonals of a rectangle are equal, but rectangles with equal diagonals have different areas.

Thanks, Bunuel.
I have one more doubt.
If I am given just the value of diagonal of a rectangle and I am asked to determine the area of that rectangle, then what is the method of determining the area of that rectangle?
Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 51121

### Show Tags

27 Dec 2017, 23:45
Deepshikha1907 wrote:
Bunuel wrote:
Deepshikha1907 wrote:

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.

You can find the area with diagonal^2/2 ONLY for squares. Yes, the diagonals of a rectangle are equal, but rectangles with equal diagonals have different areas.

Thanks, Bunuel.
I have one more doubt.
If I am given just the value of diagonal of a rectangle and I am asked to determine the area of that rectangle, then what is the method of determining the area of that rectangle?
Thanks.

You cannot get the area of a rectangle by just knowing the length of its diagonals.
_________________
Intern
Joined: 12 May 2017
Posts: 8

### Show Tags

27 Dec 2017, 23:56
Deepshikha1907 wrote:
Bunuel wrote:
What is the ratio of the area of a rectangular TV screen with a diagonal of 18'' to that of a rectangular screen with a diagonal of 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.

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.

Is the only way to know the area of a rectangle is to have its length and breadth known? So that one can use the formula area of rectangle= length*breadth?
Math Expert
Joined: 02 Sep 2009
Posts: 51121

### Show Tags

28 Dec 2017, 00:05
Deepshikha1907 wrote:
Deepshikha1907 wrote:
Bunuel wrote:
What is the ratio of the area of a rectangular TV screen with a diagonal of 18'' to that of a rectangular screen with a diagonal of 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.

Hi Bunuel,
I have encountered a genuine doubt while solving this question. Are not the diagonals of a rectangle equal in length? If it's so, then in any case the area of each rectangle can be determined using the formula 1/2*(diagonal)^2 and the ratio of their areas can be determined. This would make the 2 statements not required to answer the question itself.
Please make this clear to me. I am really confused.
Thanks.

Is the only way to know the area of a rectangle is to have its length and breadth known? So that one can use the formula area of rectangle= length*breadth?

There are also other cases. For example, the length of the diagonal and adjacent angles, which in turn will give you the length of the sides...
_________________
Manager
Joined: 28 Jun 2018
Posts: 67
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4

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05 Dec 2018, 02:22
For those who need more clarity on concepts tested in this sum -

Property - In two similar triangles, the ratio of their areas is the square of the ratio of their sides.

Take example of $$3-4-5$$ triangle. Area will be $$6$$.

Now if its a $$6-8-10$$ triangle. Area will be $$24.$$

Ratio of sides =$$6/3 = 8/4 = 10/5 = 2$$
Ratio of area = $$24/6 = 4$$

Hence (Ratio of sides)$$^2$$ = Ratio of the area

For statement 2 -
Special note on right angled triangles. These triangles follow 4 cases on similarity -
Case 1 - Side - Angle - Side case
Case 2 - At least 2 angles are proportional
Case 3 - All sides are proportional
Case 4 - Hypotenuse - Leg condition : If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar.

Bonus note - In two similar triangles, their perimeters and corresponding sides, medians and altitudes will all be in the same ratio.
>> !!!

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Intern
Joined: 21 Aug 2018
Posts: 2

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09 Dec 2018, 09:02
Since we know area of rectangle can be d1*d2/2 or d1^2/2. Isn't the information in the question enough?
Re: M10-05 &nbs [#permalink] 09 Dec 2018, 09:02

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# M10-05

Moderators: chetan2u, Bunuel

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