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ABCG and CDEF are squares with the same area that touch at p

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Carcass
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ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   25 Nov 2020, 03:19
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ABCG and CDEF are squares with the same area that touch at point C. \(∠BCD\) is a right angle.

Quantity A
Quantity B
3 times the length of AB
The length of AE



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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A
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salvador1
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Re: ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   23 Dec 2020, 03:16
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If the area of the squares is the same, they must have the same lenght.

Choice A is 3 times AB.

Choice B can be found by tracing a triangle from A to E. Finding the hypothenus of one side AB and another side 2AB. Thus its \sqrt{5}*AB which is less than 3AB
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ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   03 Jun 2021, 04:52
salvador1 wrote:
If the area of the squares is the same, they must have the same lenght.

Choice A is 3 times AB.

Choice B can be found by tracing a triangle from A to E. Finding the hypothenus of one side AB and another side 2AB. Thus its \sqrt{5}*AB which is less than 3AB




I did not understand sir, can you please elaborate?

Carcass sir, please provide official solution, i stuck :cry:
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Re: ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   07 Jun 2021, 04:58
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Draw it! You should end up with two squares oriented the same way touching at C. The squares have the same area, so their sides must be the same length. Plug in a side length for the squares to simplify the comparison—try 2. A square cut in half along its diagonal yields a pair of 45-45-90 triangles, so these two squares with sides of 2 each have diagonals of \(2 \sqrt{2}\) Diagonals AC and CE connect to form segment AE. Quantity A is 3 × 2 = 6, and Quantity B is \(2 \sqrt{2}+ 2 \sqrt{2} = 4 2 = 4 (1.4)=5.6\)

A is the answer
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Re: ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   07 Jun 2021, 05:17
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I did this and got different answer. What's wrong in this approach Carcass sir
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Re: ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   07 Jul 2021, 23:49
if we know ∠bcg and ∠acf are 90..then ∠bcd and ∠gcf are also 90...change your dig. accordingly, you'll see.
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Re: ABCG and CDEF are squares with the same area that touch at p [#permalink] New post   08 Jul 2021, 22:03
Richa1993 wrote:
if we know ∠bcg and ∠acf are 90..then ∠bcd and ∠gcf are also 90...change your dig. accordingly, you'll see.

Can you please upload a photo, I still could not get it .
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