The following question have three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. In the figure, find the value of EF. Statement I: DB = 125 cm and ΔDOE is an equilateral triangle. Statement II: CD = 35 cm and AB = 75 Statement III: AB II EF II DC and DE : EA = CF : FB = 2 : 3.?

Option 4 : Statement II and Statement III together are sufficient to answer the question.

Statement II and III:

AB II EF II DC and DE : EA = CF : FB = 2 : 3;

∴ It signifies that ΔDEO and ΔDAB are similar and ΔBFO and ΔBCD are similar.

We know CD = 35 cm and AB = 75;

∴ Values of EO and FO can be determined by the property of similar triangles (Ratio of respective sides is equal).

Statement I:

DB = 125 cm and ΔDOE is an equilateral triangle

Combining this with statement III, we can get the value of DO (by the property of similar triangles);

And the value of EO = DO (Given that ΔDOE is an equilateral triangle);

But the value of FO can’t be determined.

∴ Statement II and Statement III together are sufficient to answer the question