In a triangle PQR, RS intersects PQ at point S. The sides of the triangle QR = 36 cm, SQ = 27 cm, RS = 18 cm and ∠QRS = ∠QPR. What is the ratio of the perimeter of ∆PRS to that of ∆QSR?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
According to the given question,
In ∆PQR and ∆QSR,
∠QRS = ∠QPR
∠Q = ∠Q (common)
∆PQR ~ ∆QSR by AA similarity,
QS/QR = RS/PR
⇒ 27/36 = 18/PR
⇒ PR = 24 cm
Also, PQ/QR = QR /QS
⇒ (27 + PS)/36 = 36/27
⇒ PS = 48 - 27 = 21 cm
Now, Required ratio = (24 + 18 + 21)/(27 + 18 + 36)
⇒ 63 : 81 = 7 : 9