Question

triangle PQR ~triangle STU QR=8cm,TU=12 cm,A(triangle PQR)=128cm2 find area of triangle stu​

Answer 1

Given :  ΔPQR ≈ ΔSTU  

QR = 8 cm

TU = 12 cm

Ar( ΔPQR)  = 128 cm²

To Find : Ar( ΔSTU)      area of triangle stu​

Solution:

ΔPQR ≈ ΔSTU  

=>  Ar( ΔSTU)  / Ar( ΔPQR)   = ( TU/QR)²

Ratio of area of similar triangle is square of ratio of corresponding sides

=> Ar( ΔSTU)  /128   = ( 12/8)²

=> Ar( ΔSTU)  /128   = ( 3/2)²

=> Ar( ΔSTU)  /128   =9/4

=> Ar( ΔSTU) = 128  * 9/4

=>  Ar( ΔSTU) =32  * 9

=>  Ar( ΔSTU) =288  cm²

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