Q7 of 49 Page 25

In figure 1.66, seg PQ || seg DE, A(Δ PQF) = 20 units, PF = 2 DP, then find A(DPQE) by completing the following activity.

A(Δ PQF) = 20 units, PF = 2 DP, Let us assume DP = x. ∴ PF = 2x



In Δ FDE and Δ FPQ,


∠FDE ≅ ∠ .......... corresponding angles


∠FED ≅ ∠ ......... corresponding angles


∴ Δ FDE ~ Δ FPQ .......... AA test



A(Δ PQF) = 20units,PF = 2DP,Let us assume DP = x,∴ PF = 2x


⇒ DF = DP + PF = x + 2x = 3x


In Δ FDE & Δ FPQ


∠ FDE ≅ ∠ FPQ (Corresponding angles)


∠ FEP ≅ ∠ FQP (Corresponding angles)


∴ Δ FDE~ Δ FPQ (AA Test)


∴


A(Δ FDE) = A(ΔFPQ) = × 20 = 45


A(□DPQE) = A (Δ FDE) - A(ΔFPQ)


= 45-20


= 25 sq.unit.


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