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24 Nov 2018, 10:10
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C
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Difficulty:
45%
(medium)
Question Stats:
77% (03:28) correct
23%
(03:33)
wrong
based on 132
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In the given figure, if QR = 15 cm, PR= 3 cm and RT =5 cm. If QS = ST, ∠STQ = 60 deg and PT is a prime number greater than 5, then which of the following could be the value of QS?
A) 3
B) 4
C) 14
D) 21
E) 25
Attachment:
Q10.jpg [ 9.3 KiB | Viewed 5227 times ]
24 Nov 2018, 10:33
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Since Angle STQ = 60 deg and QS = ST, angle TQS = 60 deg, so the third angle has to be 60 deg, making triangle QTS an equilateral triangle.
In triangle RPT: PR = 3, TR = 5, so third side PT has to satisfy: (5-3) < PT < (5+3) i.e. 2 < PT < 8, but PT is a prime number greater than 5, hence PT has to be 7!
In triangle PTQ: PQ = 15 - 3 = 12, PT = 7, so third side QT has to satisfy: (12-7) < QT < (12+7) i.e. 5 < QT < 19. Since QT = QS, we get 5 < QS < 19.
Only option in this range is 14.
hence Option C
In triangle RPT: PR = 3, TR = 5, so third side PT has to satisfy: (5-3) < PT < (5+3) i.e. 2 < PT < 8, but PT is a prime number greater than 5, hence PT has to be 7!
In triangle PTQ: PQ = 15 - 3 = 12, PT = 7, so third side QT has to satisfy: (12-7) < QT < (12+7) i.e. 5 < QT < 19. Since QT = QS, we get 5 < QS < 19.
Only option in this range is 14.
hence Option C
24 Nov 2018, 10:54
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C.
Since ST=QS so angle QTS = angle TQS
And since angle STQ is 60 degree....and other two angle are same so both will be 60 degree and triangle QTS is equilateral triangle.
So QS =QT.
For length of QT
In traingle QTR QR=15 and RT =5.
Since the theorem that sum of two sides is greater than the third side...
Assuming QT is larger side...so QR + RT should be greater than QT
10+5 =15.
So it should be between 10 to 15.
So option C.
In another case if we QR to be longest side in that case sum of QT and RT should be greater than 10.
For that QT should be greater than 5.
Which is not provided in option.
Posted from my mobile device
Since ST=QS so angle QTS = angle TQS
And since angle STQ is 60 degree....and other two angle are same so both will be 60 degree and triangle QTS is equilateral triangle.
So QS =QT.
For length of QT
In traingle QTR QR=15 and RT =5.
Since the theorem that sum of two sides is greater than the third side...
Assuming QT is larger side...so QR + RT should be greater than QT
10+5 =15.
So it should be between 10 to 15.
So option C.
In another case if we QR to be longest side in that case sum of QT and RT should be greater than 10.
For that QT should be greater than 5.
Which is not provided in option.
Posted from my mobile device
