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Rectangular region QRST is divided into four smaller rectang
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Updated on: 01 Jul 2021, 19:42
Updated on: 01 Jul 2021, 19:42
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Rectangular region QRST is divided into four smaller rectangular regions, each with length l and width w.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{QR}{QS}\) |
\(\frac{3}{4}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Attachments
Bildschirmfoto 2017-03-24 um 23.43.08.png [ 26.44 KiB | Viewed 4360 times ]
Originally posted by HarveyKlaus on 24 Mar 2017, 14:44.
Last edited by rx10 on 01 Jul 2021, 19:42, edited 4 times in total.
Last edited by rx10 on 01 Jul 2021, 19:42, edited 4 times in total.
Edited the question
Re: Rectangular region QRST is divided into four smaller rectang
[#permalink]
25 Mar 2017, 08:23
25 Mar 2017, 08:23
Expert Reply
Please post the question in the right format. Thnk you for your collaboration.
Regards
Regards
Re: Rectangular region QRST is divided into four smaller rectang
[#permalink]
01 Apr 2017, 04:31
01 Apr 2017, 04:31
1
I think the question should have the Quantity 'A' asking for the ratio between QR/RS or QR/QT
In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)
Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles
QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)
Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect
So RS = x + 3x = 4x
Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B
Thank you
Correct me in case of any mistakes
In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)
Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles
QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)
Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect
So RS = x + 3x = 4x
Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B
Thank you
Correct me in case of any mistakes
Re: Rectangular region QRST is divided into four smaller rectang
[#permalink]
03 Apr 2017, 22:01
03 Apr 2017, 22:01
1
prasanna kumar wrote:
I think the question should have the Quantity 'A' asking for the ratio between QR/RS or QR/QT
In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)
Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles
QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)
Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect
So RS = x + 3x = 4x
Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B
Question is asking about QS= ??
Thank you
Correct me in case of any mistakes
In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)
Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles
QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)
Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect
So RS = x + 3x = 4x
Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B
Question is asking about QS= ??
Thank you
Correct me in case of any mistakes
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: Rectangular region QRST is divided into four smaller rectang
[#permalink]
06 Apr 2017, 07:38
06 Apr 2017, 07:38
2
Expert Reply
HarveyKlaus wrote:
Rectangular region QRST is divided into four smaller rectangular regions, each with length l and width w.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{QR}{QS}\) |
\(\frac{3}{4}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Now we can see from the figure that \(QR = 3 \times w\) and RS is \(RS= l+w\)
Now \(QS =\sqrt{QR^2 + RS^2}=\sqrt{(l+w)^2 + (3w)^2}\)
So ratio \(QR:QS=3w:\sqrt{(l+w)^2 + (3w)^2}=3w:\sqrt{(4w)^2 + (3w)^2}= \frac{3}{5}\).
Hence option B is correct.
_________________
Sandy
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Re: Rectangular region QRST is divided into four smaller rectang
[#permalink]
25 Apr 2017, 12:10
25 Apr 2017, 12:10
We can see from the figure that QR =3w . Also, it is clear that L=3w since ST = L = QR .
Now, QS = Sq.root(QR^2 + RS^2) = Sq.root[(L+w)^2 + (3w)^2] = Sq.root[(3w+w)^2 + (3w)^2] = Sq.root(25w^2) = 5w.
Therefore , QR/QS = 3w/5w = 3/5 . Given option B i.e. 3/4 is greater than 3/5. Answer is B.
Now, QS = Sq.root(QR^2 + RS^2) = Sq.root[(L+w)^2 + (3w)^2] = Sq.root[(3w+w)^2 + (3w)^2] = Sq.root(25w^2) = 5w.
Therefore , QR/QS = 3w/5w = 3/5 . Given option B i.e. 3/4 is greater than 3/5. Answer is B.
Re: Rectangular region QRST is divided into four smaller rectang
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22 May 2022, 06:18
22 May 2022, 06:18
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