Question

$\triangle ABC \sim \triangle DEF$. If BC = 3 cm, EF = 4 cm and ar($\triangle ABC$) = 54 $cm^{2}$, then ar([tex] \triangle DEF [/tex) =
(a) $108 cm^{2}$
(b) $96 cm^{2}$
(c) $48 cm^{2}$
(d) $100 cm^{2}$

Answer 1

Answer:

The ar( ΔDEF) is 96 cm².

Among the given options option (b) is 96 cm² is the correct answer.

Step-by-step explanation:

Given:

ΔABC ~ ΔDEF.

Area of ΔABC = 54 cm².

BC  = 3 cm

EF = 4 cm

ar(ΔABC)/ar( ΔDEF) = (BC/EF)²

[The ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.]

54/ar( ΔDEF) = 3²/4²

54/ar( ΔDEF) = 9/16

9/16 = 54 /ar( ΔDEF)  

9 ar( ΔDEF) = 54 × 16

ar( ΔDEF) = (54 × 16)/9

ar( ΔDEF) = (6 × 16)

ar( ΔDEF) = 96 cm²

Hence, the ar( ΔDEF) is 96 cm².

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

△ABC∼△DEF . If BC = 3 cm, EF = 4 cm and ar(\triangle ABC△ABC ) = 54 cm^{2}cm

2

, then ar(\triangle DEF [/tex) = (a) [tex] 108 cm^{2}△DEF[/tex)=(a)[tex]108cm

2

(b) 96 cm^{2}96cm ✔✔

2

(c) 48 cm^{2}48cm

2

(d) 100 cm^{2}100cm

2