Question

In the adjoining figure segPQ||segBC,AP:PB=3:4 IFA(PQCB)=160,then find A(∆ABC)

Answer 1

Area of  ΔABC = 196 cm² if AP:PB=3:4  , PQ || BC , A(PQCB)=160,then find A(∆ABC)

Step-by-step explanation:

Let say Area of ∆ABC = A

PQ ║ BC

=> ΔAPQ ≈ ΔABC

AP/AB  =  AP/(AP + PB)  =  3/(3 + 4) = 3/7

Area of  ΔAPQ  / Area of  ΔABC =  (3/7)²

=> Area of  ΔAPQ  / Area of  ΔABC = 9/49

A(PQCB)= Area of  ΔABC - Area of  ΔAPQ

=> 160 =  Area of  ΔABC - (9/49)Area of  ΔABC

=> 160 = (40/49)Area of  ΔABC

=> Area of  ΔABC = 196 cm²

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