Х 0 1 2 3 y 4 6 9 13.5 What is the common ratio?
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It is given that area( Δ ab c) =6 square units.
Also ab║d e
⇒b d =4 b c
I have depicted picture below.
Consider Δ cde in which points a and b are in the interior such that ab║de.
So, as you know that if in a triangle line joining two points is parallel to third side then the two sides are proportional.i.e
⇒ca/ae =cb / bd
Also, ∠ c is common.
∴Δcab is similar to Δ cde.
As we know if ratio of areas of two similar triangles is square of their corresponding sides.
=
⇒6/Δcde =1/4
⇒Ar (Δ cde)=6×4
Ar (Δ cde) =24 square centimeter
