Question

In triangle ABC , DE//BC.If DE:BC=3:5, then find the value of A(∆ADE) :A(DBCE)​

Answer 1

Answer:

The value of Ar.DBCE:Ar.△ADE = 16:9

Step-by-step explanation:

In △s, ABC and ADE,

∠BAC=∠DAE(Common)

∠ADE=∠ABC(Corresponding angles of parallel lines)

∠AED=∠ACB(corresponding angles of parallel lines)

Therefore, △ABC∼△ADE

For similar triangles,

ratio of area of triangles = ratio of square of corresponding sides

Hence,

Ar.△ABD/Ar.△ADE = BC²/DE²

Ar.△ABD/Ar.△ADE = 5×5/3×3

Ar.△ADE+Ar.DBCE/Ar.△ADE = 9×25

25(Ar.△ADE) = 9(Ar.△ADE)+9(Ar.DBCE)

16(Ar.△ADE) = 9(Ar.DBCE)

Ar.DBCE/Ar.△ADE = 16/9