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The area of PQR

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The area of PQR [#permalink] New post   09 Jun 2022, 03:00
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Quantity A
Quantity B
The area of \(\triangle PQR\)
Half the area of a circle of radius x



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

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B
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piorachid
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Re: The area of PQR [#permalink] New post   10 Jun 2022, 09:10
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The area of triangle PQR can be expressed as (PR*x)/2.
Half the area of a circle with radius x can be expressed as pi(x^2)/2.
The diagram shows that PR=2x.
Thus, the area of the triangle can be rewritten as (2x)x/2 or 2x^2/2.
Now we can clearly see that 2(x^2) < pi(x^2).
Therefore, B is greater.
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Re: The area of PQR [#permalink] New post   12 Jun 2022, 09:24
Area of Triangle PQR is \(\frac{1}{2}*2x*x\) = \(x^2\)

Area of a circle of radius r is \(pi*x^2\)

\(pi*x^2\) > \(x^2\)

Answer is (B)
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Re: The area of PQR [#permalink]
12 Jun 2022, 09:24
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