# 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

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