In the figure above, a circle is tangent to a pair of opposite sides o

Hi,

Area of parallelogram = Base * height...
Base can be taken either of the parallel sides...
we are given one base as 58, but if you look at the height, it is nothing BUT the diameter of circle as both the opposite sides are tangent to circle..

lets see the statements

(1) The perimeter of the parallelogram is 120 cm.
we know the length of the other side, BUT we cannot deduce the HEIGHT..
Also with All sides known, there can be various types of llgm possible, which will have different areas..
Insuff

(2) The circumference of the circle is "pi".
From the circumference we can find the DIA, which is nothing BUT the height
2*pi*r = pi, SO DIA = 1..
so area = 1*58 = 58
Suff

B
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If we modify the original condition and the question, the area of the parallelogram can be found if we find the height of the parallelogram. Hence, we only have to find the diameter of the circle. However, from the condition 2), we get 2r=d(diameter)=1 from 2pi r=pr. The answer is unique and the condition is sufficient. Hence the correct answer is B.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

Chetan, I assume by DIA you mean diameter, not diagonal. Could you please explain why 2pr = p? I didn't see how you got to diameter = 1. Thanks!

2pR=p

p = pi so if we divide p on both sides we get 2R=1

D = 2r, so D = 1.

In this case the diameter is equal to the height of the parallelogram, so base (58) x height (1) = area (58)

Area of parallelogram = Base*height.

We need to find out height.

(1) The perimeter of the parallelogram is 120 cm.
We can calculate length of other two sides of parallelogram, but not the height. Not Sufficient.

(2) The circumference of the circle is "pi".
If 2 pi r= pi
r=1/2 cm
D= 1 cm, which is height of parallelogram.
Sufficient

B is the answer
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1. Yes, mitko20m. DIA is diameter.
2. 2*pi*r = circumference of a circle . This is a direct formula.
circumference of the circle = pi (given in st2.)

Hope it's clear.

Since we are looking for the area of the parallelogram we need to have a value for the base and the height. We are given a value of 58 for the base from the prompt so we are looking for the height from either statement one or statement 2.

1) The perimeter of the parallelogram is 120cm.- this does not give us any information that would help us find the height so eliminate
2) The circumference of the circle is "pi" - we know that circumference =2pi*r or C=pi*Diameter. From this statement we know that the diameter =1 which means height of the parallelogram is equal to 1. The area of the parallelogram is 58*1 so we know we can solve for the area with this information, therefore statement B is sufficient.

Given: In the figure above, a circle is tangent to a pair of opposite sides of a parallelogram. The length of each of these opposite sides is 58 cm.
Asked: What is the area of the parallelogram in square centimeters?

Since base of parallelogram is known = 58 cm, height of parallelogram is required to determine its area.

(1) The perimeter of the parallelogram is 120 cm.
The other side = (120 - 2*58)/2 = 2 cm
But still height of parallelogram is unknown
NOT SUFFICIENT

(2) The circumference of the circle is "pi".
Height of parallelogram = Diameter of the circle = 1 cm
Area of parallelogram = 58*1 = 58 cm^2
SUFFICIENT

IMO B

Won't the height of the parallelogram be fixed if the sides are known? I am slightly confused here.

Can there be parallelograms with different heights possible? I am not able to think of such cases. Would really appreciate your help!

chetan2u Bunuel Would really appreciate your help here. Thanks in advance!

The sides are 58 and 2.
If the side 2 is perpendicular on 58, then height is 2.

But say the angle between 58 and 2 is 45, then the perpendicular will be \(\sqrt{2}\).
When the angle is just 1, then the height will be negligible as the opposite sides 58 will be hugging each other.
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avigutman Bunuel chetan2u
Is STATEMENT Complete?: (2) The circumference of the circle is "pi".

Wouldn't different unit of circumference, give different area?
circumference of circle drawn could be 3.14 mm, cm or any unit.

\(\pi\) is a constant number or ratio of circumference to diameter.

Say \(\pi\) had a unit, then circumference \(2\pi r \) would have a unit cm*cm, which would not be correct as circumference is in cm/m/mm etc

BUT since we are talking of circumference in the statement, the statement should read pi cm
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