Question

....................
PLEASE SOLVE THIS QUESTION TOMORROW IS MY BOARDS...
BEST ANSWER WOULD BE MARK AS BRAINLIEST
❤❤✌✌✌ ​

Answer 1

Step-by-step explanation:

Given: DE║BC  & AD/DB = 3/2

(i) AD/AB = AD/AD+DB = 3/2+3 = 3/5

Since DE parallel to BC (by Basic Proportionality Theorem)

DE/BC = AD/AB = 3/5

(ii)

In ΔDEF & ΔCBF

<DFE = <CFB  [vertically opposite angles]

<FDE = <FCB   [parallel lines -interior opposite angles are equal]

<DEF = <CBF  [interior opposite angles of a parallel line]

BY AAA criterion, ΔDEF & ΔCBF are SIMILAR

EF/FB = DE/BC = 3/5    [In similar triangles corresponding sides are proportional]

(iii) ΔDFE & ΔBFC are similar

Area of DFE/Area of BFC = DE²/BC² = 3²/5² = 9/25

[In SIMILAR triangles, the ratio of areas is directly proportional to square of corresponding sides]