Question

In the fig., PQ ‖ BC and AP: PB = 1 : 2. Find ar( apq)/ar(abc)

Answer 1

Answer:

We form our diagram from given information , As :

Here BC | | PQ and APPB = 12 , So

⇒APAB = APAP + PB = 11 + 2 = 13

In ∆ ABC and ∆ APQ

∠ BAC = ∠ PAQ ( Same angle )

And

∠ ABC = ∠ APQ ( Corresponding angles as BC | | PQ and AB as transversal line )

So,

∆ ABC ~ ∆ APQ ( By AA rule )

We know ratio of area of similar triangles :

Area of ∆ APQArea of ∆ ABC = (Corresponding side )2(Corresponding side )2⇒Area of ∆ APQArea of ∆ ABC = (AP)2(AB )2⇒Area of ∆ APQArea of ∆ ABC = (1)2(3 )2⇒Area of ∆ APQArea of ∆ ABC = 19⇒Area of ∆ APQ : Area of ∆ ABC = 1 : 9 ( Hence proved )

Step-by-step explanation:

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