Correct Answer - Option 4 :
\(\frac{7\sqrt3}{5}cm\)
Given :-
ΔDEF ~ ΔABC
Area of ΔABC is 9 cm2 and ΔDEF IS 12 cm2
BC = 2.1 cm
Concept :-
Relation among areas, side, altitude and perimeters of similar triangle
(area of ΔABC/area of ΔDEF) = (AB/DE)2 = (BC/EF)2 = (AC/DF)2
Calculation :-
Let EF = x cm
⇒ (9/12) = (2.1/x)2
⇒ x2 = (2.1 × 2.1 × 12)/9
⇒ x2 = (7 × 7 × 3)/25
⇒ x = √((7 × 7 × 3)/25)
⇒ x = (7√3)/5
⇒ EF = (7√3)/5 cm
∴ EF is (7√3)/5 cm