In ∆ABC AB || DE. if AD = 7 cm DC = 3.5 cm and area of ABED is 96 sq. cm. find area of ∆ABC
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△ABC, DE∥BC
⇒ ∠B=∠D [ Corresponding angles ]
⇒ ∠C=∠E [ Corresponding angles ]
⇒ ∠A=∠A [ Common angle]
∴ 4△ABC∼△ADE [ By AAA criteria ]
(i)
area(△ADE)
area(△ABC)
=(
DE
BC
)
2
[ Ratio of areas of two similar triangles is equal the ratio of squares of their corresponding sides. ]
∴
16
area(△ABC)
=(
4
6
)
2
∴ area(△ABC)=
16
36×16
∴ area(△ABC)=36cm
2
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