Question

in Fig. 9.41, area of ∆PQR is 20 cm2 and area of ∆PQS is 44 cm2. Find the length RS, if PQ is perpendicular to QS and QR is 5cm​

Answer 1

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Class 9>>Maths>>Heron's Formula>>Area of a Triangle>>In Fig., area of triangle PQR is 20 cm^2

Question

In Fig., area of triangle PQR is 20cm2 and area of triangle PQS is 44cm2. Find the length RS. if PQ is perpendicular to QS and QR is 5cm.

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Solution

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Given, Area of triangle PQR=20sq.cm 

Area of triangle PQS=44sq.cm

From figure ∠Q=90o

So, Area of triangle PQR, 

⇒20=21×PQ×QR=21×PQ×5

⇒PQ=540=8cm 

Now,

Area of triangle PQS, 

⇒44=21×PQ×QS=21×8×QS

⇒QS=844×2=11cm

Now, RS=QS−QR=11−5=6cm