Q5 of 49 Page 25

Areas of two similar triangles are 225 sq.cm & 81 sq.cm. If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle.

Let area of one(bigger) triangle be ‘A’, other(smaller) triangle be ‘B’,corresponding side of smaller triangle be ‘a’ and bigger triangle be ‘b’.

⇒ (By theorem)


And a = 12cm, A = 225 sq.cm, B = 81 sq.cm ……(Given)


⇒


⇒ b2 =


⇒ b = √400


⇒ b = 20 cm


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Δ ABC and ΔDEF are equilateral triangles. If A(ΔABC) : A(ΔDEF) = 1 : 2 and AB = 4, find DE.

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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