Question

in the given fig, D and Eare the midpoints of AB and AC respectively ifDE=4cm, then the value BC is​

Answer 1

Answer:

In △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)=(DEBC)2     [ Ratio of areas of two similar triangles is equal the ratio of squares of their corresponding sides. ]

∴  16area(△ABC)=(46)2

∴  area(△ABC)=1636×16

∴  area(△ABC)=36cm2

(ii)  area(△ADE)area(△ABC)=(DEBC)2     [ Ratio of areas of two similar triangles is equal the ratio of squares of their corresponding sides. ]

∴  25area(△ABC)=(48)2

∴  area(△ABC)=16

Step-by-step explanation:

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