Question

In triangle PQR,. Ps /QR,Ps=11cm, and area of triangle PQR=77 sq.cm If area of triangle PSR=3:4,find QS and SR​

Answer 1

Given : In triangle PQR,. Ps ⊥ QR, PS=11 cm, and area of triangle PQR=77 sq.cm

area of triangle PQS :  area of triangle PSR : =3:4

To Find QS and SR​

Solution:

area of triangle PQR= (1/2) * QR * PS

=> (1/2) * QR * 11 = 77

=> QR = 14 cm

area of triangle PQS  = (1/2) QS * PS

area of triangle PSR  = (1/2) SR * PS

(1/2) QS * PS :  (1/2) SR * PS =  3: 4

=>    QS : SR = 3 : 4

QS = 3x and SR = 4x

QS + SR = QR

=> 3x + 4x = 14

=> 7x = 14

=> x = 2

QS = 3x = 6

SR = 4x =  8

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