Question

find the ratio of triangle ABC and triangle DEF

Answer 1

Answer:

Sol:

Given that D, E and F are the mid-points of BC, CA and AB respectively, then from the mid-point theorem

EF = BC / 2, DE = AB / 2, DF = AC / 2.

But Δ ABC ~ Δ DEF

Ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides  

⇒ Area of triangle ABC / Area of triangle DEF = BC2 / EF2

⇒ Area of triangle ABC / Area of triangle DEF = (2EF)2 / EF2

⇒ Area of triangle ABC / Area of triangle DEF = 4 / 1.

∴Ratio of the areas of triangle DEF and triangle ABC is 1 : 4.

Step-by-step explanation:

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