Question

In the adjoining figure,
PQ ⊥ BC, AD ⊥ BC,
PQ = 4, AD = 6
Write down the following ratios.
(i)`(A(ΔPQB))/(A(ΔADB))`

(ii)`(A(ΔPBC))/(A(ΔABC))`

Answer 1

(i) In ΔPQB and ΔADB ,
∠B ≅ ∠B
∠PQB ≅ ∠ADB ................. (each right angle)
∴ ΔPQB ∼ ΔADB ................. (A-A test of similarty)
∴`(A(Delta PQB))/(A(DeltaABC)) = (PQ)^2/(AD)^2 = 4^2/6^2 = 16/36 = 4/9 `.......(Theorem of areas of similar triangle)

(ii) `(A(DeltaPBC))/(A(Delta ABC)) =(PQ)/(AD) = 4/6 = 2/3`.....(triangles having equal bases)