Question

$Inthefigure,givenalongside,PBandQAareperpendicularstothelinesegmentAB.IfPO=3cm,QO=4.5cmandareaof△POB=60c{m}^2,findtheareaof△QOA.$

• A. 135 cm²
• B. 130 cm²
• C. 270 cm²
• D. 70 cm²

Answer 1

The correct option is A

135 cm²

$in△POBand△QOA1.\angle POB=\angle QAO\left[Each{90}^0\right]2.\angle POB=\angle QOA\left[Veticallyoppositeangles\right]\Rightarrow △POB\sim △QOA[ByA.A]\frac{Ar.\left(△POB\right)}{Ar.\left(△POB\right)}=\frac{P{O}^2}{Q{O}^2}[Ratiobetweentheareasoftwosimilartrianglesisequaltotheratiobetweenthesquaresofthecorrespondingsides]\Rightarrow \frac{60}{Ar.\left(△QOA\right)}=\frac{3^2}{{4.5}^2}\Rightarrow Ar.\left(△QOA\right)=\frac{69\times 20.25}{9}c{m}^2=135c{m}^2$