KVPY SA Exam 2018 Question Paper

Question : 11 of 80

Marks: +1, -0

Let PQR be a triangle in which PQ = 3. From the vertex R, draw the altitude RS to meet PQ at S. Assume that RS =

√3

and PS = QR. Then PR equals

Solution:

PS = QR

PS + SQ = 3

∆\RSQ \;\;\;\;\;\SQ = 3 -PS = 3 -QR

QR^2 = RS^2 + SQ^2

QR^2 = 3 + (3 -QR)^2

QR^2 = 3 + 9 + QR^2 -6QR

6QR = 12

QR = 2

SQ = 1, PS = 2

∆\RSP

PR^2 = RS^2 + PS^2

= 3 + 4

PR^2 = 7

PR = √7

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