Question

If in the given figure, DE parallel to BC, 2DE=BC, 3GH=DE, then find the area ratio of ABC and DEF​

Answer 1

Since DE || BC, by Thales theorem AD/DB = AE/EC Therefore, both AD/DB and AE/EC = 1: 2 So AD:AB = 1:3 or AB:AD = 3:1

The triangles are similar by SAS axiom. Hence the areas of the triangles are in the ratio of squares of corresponding sides.

Therefore, the ratio of area of Δ ABC to the area of Δ ADE = 3^2:1^2 = 9:1.

Answer 2

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Since DE || BC

, by Thales theorem AD/DB = AE/EC

Therefore, both AD/DB

and

AE/EC = 1: 2

So AD:AB = 1:3

or

AB:AD = 3:1

The triangles are similar by SAS axiom. Hence the areas of the triangles are in the ratio of squares of corresponding sides.

Therefore, the ratio of area of Δ ABC to the area of Δ ADE = 3^2:1^2 = 9:1

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thanks⭐⭐⭐⭐⭐