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90 < x < 180
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29 Dec 2018, 10:15
29 Dec 2018, 10:15
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Question Stats:
42% (01:17) correct
57% (01:05) wrong based on 135 sessions
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#GREpracticequestion The perimeter of AOB.jpg [ 13.43 KiB | Viewed 6522 times ]
\(90 < x < 180\)
Quantity A |
Quantity B |
The perimeter of \(\triangle AOB\) |
17 |
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.
Re: 90 < x < 180
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08 Jan 2019, 17:39
08 Jan 2019, 17:39
2
Answer: A
90< x < 180
If x = 90, then the OAB would turn into a right traingle and we will have:
AO = OB = 5
AB = √(√5^2 + √5^2) = 5√2
Perimeter of OAB : 5 + 5 + 5√2 = 5(2+√2) that is a little bit bigger than 17(B)
__
If x is a little bit less than 180 (because if x=180, then there won’t be any traingle but two parallel lines:
In this case, OA=OB are still the same size(5) but more the x is, the more the AB would be. So the perimeter is even bigger than when x=90.
In general the perimeter of AOB is 10+AB. The least possible value for AB when 90< x < 180, occurs when x=90 and in this case, perimeter of the triangle is bigger than 17.
90< x < 180
If x = 90, then the OAB would turn into a right traingle and we will have:
AO = OB = 5
AB = √(√5^2 + √5^2) = 5√2
Perimeter of OAB : 5 + 5 + 5√2 = 5(2+√2) that is a little bit bigger than 17(B)
__
If x is a little bit less than 180 (because if x=180, then there won’t be any traingle but two parallel lines:
In this case, OA=OB are still the same size(5) but more the x is, the more the AB would be. So the perimeter is even bigger than when x=90.
In general the perimeter of AOB is 10+AB. The least possible value for AB when 90< x < 180, occurs when x=90 and in this case, perimeter of the triangle is bigger than 17.
