Step-by-step explanation:

(d) 108 cm². ........................

Verified answer

Answer:

Option (c) 96cm²

Given:

∆ABC ~ ∆DEF

EF = 4cm

BC = 3cm

Area of ∆ABC = 54cm²

To Find :

Area of ∆DEF ?

Solution:

Since the ratio of Area of two similar triangle is equal to the ratio of squares of any two corresponding sides

[tex]⇒\frac{Area \: of \: ∆ABC}{Area \: of \: ∆DEF} = \frac{(BC)²}{(EF)²} [/tex]

[tex]⇒\frac{54}{Area \: of \: ∆DEF} = \frac{ {3}^{2} }{ {4}^{2} } [/tex]

[tex]⇒Area \: of \: ∆DEF = \frac{54 \times 16}{9} [/tex]

[tex]⇒Area \: of \: ∆DEF = {96cm}^{2} [/tex]

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