Q. 14.0( 5 Votes )

# Triangles ABC and DEF are similar.

(i) If area () = 16 cm^{2}, area () = 25 cm^{2} and BC = 2.3 cm, find EF.

(ii) If area () = 9 cm^{2}, area () = 64 cm^{2} 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 cm^{2}, area () = 64 cm^{2} 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) = 16cm^{2}

Area (ΔDEF) = 25cm^{2}

And BC = 2.3cm

Since, ΔABC ~ΔDEF

Then, Area (ΔABC)/Area (ΔDEF)

= BC^{2}/EF^{2} (By are of similar triangle theorem)

Or, 16/25 = (23)^{2}/ EF^{2}

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) = 9cm^{2}

Area (ΔDEF) = 64cm^{2}

And BC = 5.1cm

Since, ΔABC ~ΔDEF

Then, Area (ΔABC)/Area (ΔDEF)

= AB^{2}/DE^{2} (By are of similar triangle theorem)

Or, 9/64 = AB^{2}/(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 = AC^{2} /DE^{2}(Br area of similar triangle theorem)

(19)^{2}/(8)^{2} = 364/64

(iv) We have

Area ΔABC = 36cm^{2}

Area ΔDEF = 64 cm^{2}

DE = 6.2 cm

And , ΔABC ~ΔDEF

By area of similar triangle theorem

Area of ΔABC/Area of ΔDEF = AB^{2} /DE^{2}

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 = AB^{2} /DE^{2}

Or, (1.2)^{2}/(1.4)^{2} = 1.44x/1.96

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