Question

In the ∆ABC, DE || BC. If AB : AD = 5 : 3 then area of ∆ABC : area of ∆ADE

is​

Answer 1

Answer:

25:9

Step-by-step explanation:

In Similar triangles

The ratio of areas = The square of ratio of its sides

i.e. ratio of side --> 5:3

therefore, Ratio of area = $(5:3)^{2}$ =  25:9

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Answer 2

Given :- In the ∆ABC, DE || BC. If AB : AD = 5 : 3 then area of ∆ABC : area of ∆ADE is ?

Solution :-

given that, DE || BC .

so, in ∆ADE and ∆ABC we have,

→ ∠ADE = ∠ABC { corresponding angles.}

→ ∠AED = ∠ACB { corresponding angles.}

then,

→ ∆ADE ~ ∆ABC { By AA similarity. }

now, we know that, when two ∆'s are similar,

• Ratio of area of ∆'s = Ratio of square of their corresponding sides .

then,

→ area of ∆ABC / area of ∆ADE = AB²/AD²

→ area of ∆ABC / area of ∆ADE = 5²/3²

→ area of ∆ABC / area of ∆ADE = 25/9

→ area of ∆ABC : area of ∆ADE = 25 : 9 (Ans.)

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