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PQR is a right-angled triangle with hypotenuse QR of length 20 inches
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11 Mar 2022, 22:50
11 Mar 2022, 22:50
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PQR is a right-angled triangle with hypotenuse QR of length 20 inches and a perpendicular AP on QR.
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Maximum possible length of AP in inches |
10 |
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
Re: PQR is a right-angled triangle with hypotenuse QR of length 20 inches
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22 Mar 2022, 12:04
22 Mar 2022, 12:04
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Got this incorrect, will wait for OE
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
PQR is a right-angled triangle with hypotenuse QR of length 20 inches
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24 Mar 2022, 23:24
24 Mar 2022, 23:24
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KarunMendiratta wrote:
PQR is a right-angled triangle with hypotenuse QR of length 20 inches and a perpendicular AP on QR.
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Maximum possible length of AP in inches |
10 |
A. The quantity in Column A is greater.
B. The quantity in Column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given
OA Explanation
The length of AP is maximum when the given triangle in an Isosceles Right angled traingle.
(Refer to the figure below)
Ratio of sides in an Isosceles Right angled traingle is \(x : x : x\sqrt{2}\)
So, \(20 = x\sqrt{2}\)
i.e. \(x = 10\sqrt{2}\)
Now, let us equate the area;
\(\frac{1}{2}(x)(x) = \frac{1}{2}(20)(AP)\)
\((10\sqrt{2})(10\sqrt{2}) = 20(AP)\)
\(AP = 10\)
Col. A: 10
Col. B: 10
Hence, option C
