Triangles ABC and DEF are similar.
(i) If area (
) = 16 cm2, area (
) = 25 cm2 and BC = 2.3 cm, find EF.
(ii) If area (
) = 9 cm2, area (
) = 64 cm2 and DE = 5.1 cm, find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (
) = 36 cm2, area (
) = 64 cm2 and DE = 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of 
.
(i) We have
ΔABC ~ΔDEF
Area (ΔABC) = 16cm2
Area (ΔDEF) = 25cm2
And BC = 2.3cm
Since, ΔABC ~ΔDEF
Then, Area (ΔABC)/Area (ΔDEF)
= BC2/EF2 (By are of similar triangle theorem)
Or, 16/25 = (23)2/ EF2
Or, 4/5 = 2.3/EF (By taking square root)
Or, EF = 11.5/4
Or, EF = 2.875cm
(ii) We have
ΔABC ~ΔDEF
Area (ΔABC) = 9cm2
Area (ΔDEF) = 64cm2
And BC = 5.1cm
Since, ΔABC ~ΔDEF
Then, Area (ΔABC)/Area (ΔDEF)
= AB2/DE2 (By are of similar triangle theorem)
Or, 9/64 = AB2/(5.1)2
Or, AB = 3 x 5.1/8 (By taking square root)
Or, AB = 1.9125cm
(iii) We have,
ΔABC ~ ΔDEF
AC = 19cm and DF = 8cm
By area of similar triangle theorem
Then, Area of ΔABC/Area of ΔDEF = AC2 /DE2(Br area of similar triangle theorem)
(19)2/(8)2 = 364/64
(iv) We have
Area ΔABC = 36cm2
Area ΔDEF = 64 cm2
DE = 6.2 cm
And , ΔABC ~ΔDEF
By area of similar triangle theorem
Area of ΔABC/Area of ΔDEF = AB2 /DE2
Or, 36/64 = 6x 6.2/8 (By taking square root)
Or, AB = 4.65cm
(V) We have
ΔABC ~ ΔDEF
AB = 12cm and DF = 1.4 cm
By area of similar triangle theorem
Area of ΔABC/Area of ΔDEF = AB2 /DE2
Or, (1.2)2/(1.4)2 = 1.44x/1.96