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The figure above shows the shape of a flower bed

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by sanjib » Wed Aug 12, 2009 7:26 pm
please see the attachment for the figure.
The figure above shows the shape of a flower bed. If arc QR is a semicircle and PQRS is a rectangle with QR > RS, what is the perimeter of the flower bed ?
(1) The perimeter of rectangle PQRS is 28 feet.
(2) Each diagonal of rectangle PQRS is 10 feet long.

OA is B
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by tohellandback » Wed Aug 12, 2009 7:59 pm
are you sure the OA is B
IMO C:
my method:

1) 2(l+b)=28
l+b=14
Not suff. we can have many different values

2) l^2 +b^2=100
again there are many possible values.
combined,
l+b=14
l^2 +b^2=100
196-2lb=100
lb=48
(14-b)*b=48
b^2-14b+48=0
b=6,8
since it is given that QR>RS
b=6
l=8
you can get the perimeter now.

SUFFICIENT
The powers of two are bloody impolite!!
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by sbasha » Wed Aug 12, 2009 8:58 pm
It has to be C. If not please let us know
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by lav » Thu Aug 13, 2009 1:58 am
even my ans is C
no where in question it says that length of side QR and RS is integers
from B we know that diagonal is 10 and ques says QR>RS then two solutions are obvious ...
QR=8 RS=6 and QR=3(10)^1/2 and RS=(10)^1/2
hence its not B

but when we combine the two statements we get only on soln 8,6
Kid in Verbal :(
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by gauravgundal » Thu Aug 13, 2009 2:40 am
if the length or breadth is an integer,the answer would be B.
otherwise it is C
But nowhere it is said that len or bredth is integer. so answer is C
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by GambitOS » Thu Aug 13, 2009 4:50 am
:? I don't understand.
We need to find the perimeter of all bed, but in explanation above we find just the perimeter of rectangle. Is it not necessary to know perimeter of semicircle QR?
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by gmatpill » Thu Aug 13, 2009 9:41 am
You might be surprised, but the answer is in fact (B). Here's why.

In order to find the length of the arc, we need the length of the rectangle (the longer side). (since we know pi * diameter = circumference of circle--and here we have half of a circle)

Statement (1): given perimeter is 28 tells us that the sum of the length and width must be 14: Perimeter = 28 = 2 * (Length + Width)
So (Length + Width = 28/2 = 14

Does that help us find the length of the rectangle? No it does not.

Statement (2): The diagonal of the rectangle is 10.
What does this tell us? Well, the key here is to know that we are in a rectangle.

What do we know about rectangles? They have 90 degree corners.

What do we know about 90 degree triangles?

Well, there are 2 common types: the 3-4-5 triangle and the 5-12-13 triangle.

Here the hypotenuse is given as 10--which means this must be a 3-4-5 triangle since the "5" divides evenly into "10".

This tells us that the width must be 6 and the length must be 8.

Now that we have the length, we can easily calculate the length of the arc.

And once we have the arc we can easily calculate the total perimeter.

So yes, the answer is (B)!
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by Ian Stewart » Thu Sep 10, 2009 12:44 am
gmatpill wrote:You might be surprised, but the answer is in fact (B). Here's why.

In order to find the length of the arc, we need the length of the rectangle (the longer side). (since we know pi * diameter = circumference of circle--and here we have half of a circle)

Statement (1): given perimeter is 28 tells us that the sum of the length and width must be 14: Perimeter = 28 = 2 * (Length + Width)
So (Length + Width = 28/2 = 14

Does that help us find the length of the rectangle? No it does not.

Statement (2): The diagonal of the rectangle is 10.
What does this tell us? Well, the key here is to know that we are in a rectangle.

What do we know about rectangles? They have 90 degree corners.

What do we know about 90 degree triangles?

Well, there are 2 common types: the 3-4-5 triangle and the 5-12-13 triangle.

Here the hypotenuse is given as 10--which means this must be a 3-4-5 triangle since the "5" divides evenly into "10".

This tells us that the width must be 6 and the length must be 8.

Now that we have the length, we can easily calculate the length of the arc.

And once we have the arc we can easily calculate the total perimeter.

So yes, the answer is (B)!
This is not at all true. If the hypotenuse of a right triangle is 10, the lengths of the legs could be 6 and 8, but they could also be 1 and sqrt(99), or 3 and sqrt(91), among many other possibilities. The answer to the question in the original post is C, not B.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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