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04 Oct 2018, 02:32
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B
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Difficulty:
25%
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Question Stats:
81% (02:00) correct
19%
(02:45)
wrong
based on 103
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In the figure shown below, what is the value of K?
(A) 45
(B) 50
(C) 55
(D) 65
(E) 70
2018-10-04_1331.png [ 32.23 KiB | Viewed 2863 times ]
(A) 45
(B) 50
(C) 55
(D) 65
(E) 70
Attachment:
2018-10-04_1331.png [ 32.23 KiB | Viewed 2863 times ]
04 Oct 2018, 02:50
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Right Triangle PSR is a 5-12-13. Hence, PR=13
Right Triangle PQT= 84^2 + pq^2= 85^2 --- PQ^2=85^2-84^2
PQ^2= (85+84)(85-84)= 169
PQ=13
Hence, Triangle PQR is an isosceles triangle
since, PQ= 13 and opposite angle Q= 65degrees, similarly PR=13, hence, opposite angle R= 65degrees
180-(2*65)= 50
Ans= B
Right Triangle PQT= 84^2 + pq^2= 85^2 --- PQ^2=85^2-84^2
PQ^2= (85+84)(85-84)= 169
PQ=13
Hence, Triangle PQR is an isosceles triangle
since, PQ= 13 and opposite angle Q= 65degrees, similarly PR=13, hence, opposite angle R= 65degrees
180-(2*65)= 50
Ans= B
14 Dec 2020, 12:12
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Bunuel
In the figure shown below, what is the value of K?
(A) 45
(B) 50
(C) 55
(D) 65
(E) 70
(A) 45
(B) 50
(C) 55
(D) 65
(E) 70
Attachment:
2018-10-04_1331.png
Triangle PSR support Pythagorean Triples \(5:12:13\)
\(PR=12,\) PR is also a side of Triangle \(PRQ.\)
Triangle PQT is also a right triangle, where: \(PQ^2+QT^2=PT^2\)
\(PQ^2+84^2=85^2\)
\(PQ^2+84^2=(84+1)^2\)
\(PQ^2=84^2+2*84*1+1^2-84^2\)
\(PQ^2=168+1=169\)
\(PQ=\sqrt{163}=13\), Which is a side of Triangle \(PRQ\)
In Triangle \(PRQ\), \(PR=PQ=13\)
So, Triangle \(PRQ \) is an isosceles triangle, Whose two angles 65 each, So, the other Angle \(X=180-(65+65)=50\)
The answer is B
