Q. 14.0( 5 Votes )

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 .

Answer :

(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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