Question

in the given fig if ST||QR then the ratio of area of triangle PST and are of STRQ is?

Answer 1

Given : ST||QR

ST = 4 cm

QR = 12

To Find :  the ratio of area of triangle PST and area of STRQ

Solution:

ST || QR

in  ΔPST and ΔPQR

∠S  = ∠Q   ( corresponding angle )

∠T = ∠R   ( corresponding angle )

∠P = ∠P   ( common angle )

=> ΔPST ≈ ΔPQR

Ratio of area of similar triangle = (ratio of corresponding sides)²

=> Ar ( Δ PST) / Ar (ΔPQR)     = (ST / QR)²

=> Ar ( Δ PST) / Ar (ΔPQR)     = (4 / 12)²

=> Ar ( Δ PST) / Ar (ΔPQR)     =  1/9

=> Ar (ΔPQR)  = 9 Ar ( Δ PST)

Ar ( STRQ) = Ar (ΔPQR)  - Ar ( Δ PST) =  9 Ar ( Δ PST) - Ar ( Δ PST)

=> Ar ( STRQ) =  8 Ar ( Δ PST)

Ar ( Δ PST)  / Ar ( STRQ)  =  Ar ( Δ PST)  / 8 Ar ( Δ PST)

=> Ar ( Δ PST)  / Ar ( STRQ)  =  1/8

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