in triangle ABC Seg DE || Side AB, DC = 2BD; A(triangle CDE) =20 sq.m find A(square ABDE).
Answers
Step-by-step explanation:
correct answer for your question
Given : DE ∥ AB
DC= 2BD
Ar(∆CDE)= 20cm²
https://brainly.in/question/29487984 ( ref for figure)
To Find : Ar(□ABDE)
Solution:
DE ∥ AB
=> ∠D = ∠B and ∠E = ∠A corresponding angles
ΔCDE ~ Δ CBA using AA similarity
CD/CB = CD/(CD + BD)
= 2BD/(2BD + BD)
= 2BD/3BD
= 2/3
Ratio of area of similar triangles = ( ratio of corresponding sides)²
Area of ΔCDE /Ar of Δ CBA =( CD/CB)²
Area of ΔCDE /Ar of Δ CBA =( 2/3)²
Area of ΔCDE /Ar of Δ CBA = 4/9
Ar(∆CDE)= 20 cm²
=> 20/ Ar of Δ CBA = 4/9
=> Ar of Δ CBA = 45 cm²
Ar(□ABDE) = Ar of Δ CBA - Ar(∆CDE)
= 45 - 20
= 25
Hence Ar(□ABDE) is 25 cm²
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