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Math Expert V
Joined: 02 Sep 2009
Posts: 59622
A square, a circle and a right triangle are made to overlap so that th  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 45% (02:01) correct 55% (01:56) wrong based on 47 sessions

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A square, a circle and a right triangle are made to overlap so that the radius of the circle is equal to a side of the square and the base of the triangle. If the area of the circle is 16π, what is the ratio of the area of the square to the area of the triangle?

A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
E. It cannot be determined from information given.

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Director  G
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
A square, a circle and a right triangle are made to overlap so that th  [#permalink]

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Bunuel wrote:
A square, a circle and a right triangle are made to overlap so that the radius of the circle is equal to a side of the square and the base of the triangle. If the area of the circle is 16π, what is the ratio of the area of the square to the area of the triangle?

A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
E. It cannot be determined from information given.

area of the circle = 16$$\pi$$ = $$\pi r^2$$
r=4
area of the square =$$4^2$$ = 16
area of right triangle = $$\frac{b*h}{2}$$ , but we do not know anything about height of the triangle
therefore , the ratio cannot be determined

E
Intern  B
Joined: 07 Jun 2018
Posts: 20
Location: India
GPA: 3.9
WE: Marketing (Insurance)
Re: A square, a circle and a right triangle are made to overlap so that th  [#permalink]

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Bunuel wrote:
A square, a circle and a right triangle are made to overlap so that the radius of the circle is equal to a side of the square and the base of the triangle. If the area of the circle is 16π, what is the ratio of the area of the square to the area of the triangle?

A. 1 : 2
B. 1 : 4
C. 2 : 1
D. 4 : 1
E. It cannot be determined from information given.

Radius of circle = side of square = base of triangle

We know the radius of the circle from the area of the circle. So, other pieces of information such as the side of the square and the base of the triangle are known.

But, we don't know the perpendicular height of the triangle from information. Without which area of triangle can't be determined.

Hence, E.
Director  P
Joined: 18 Dec 2017
Posts: 829
Location: United States (KS)
Re: A square, a circle and a right triangle are made to overlap so that th  [#permalink]

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Nice trick. Fell for C. Because nothing is mentioned about the height, it can actually be infinity +1
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You are missing on great learning if you don't know what this is: Project SC Butler Re: A square, a circle and a right triangle are made to overlap so that th   [#permalink] 29 Nov 2019, 09:31
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