Question

Let ∆ABC~ ∆DEF and their areas be respectively, 64cm^2 and 121cm^2. If EF=15.4cm,find BC

Answer 1

Answer:

Since ∆ABC is similar to ∆DEF:

$\tt{ar(\frac{\triangle ABC}{\triangle DEF}) = (Ratio\: of \: sides)^{2}}$

=> 64/121 = (x/15.4)^2

=> 8/11 = x/15.4

=> x = 11.2 cm

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Answer 2

$\underline \mathbb{SOLUTION}$

$\bold{\huge{\fbox{\color{Red}{Given}}}}$

ΔABC ~ ΔDEF

$\frac{ar(abc)}{ar(def)} = \frac{ {bc}^{2} }{ {ef}^{2} }$

(From basic proportioanality theorem,)

$= > \frac{64}{121} = \frac{ {bc}^{2} }{ {ef}^{2} }$

$= > \frac{bc {}^{2} }{ {ef}^{2} } = (\frac{8}{11} ){}^{2}$

$= > \frac{bc}{ef} = \frac{8}{11}$

$= > bc = \frac{8}{11} \times ef$

$= > bc = \frac{8}{11} \times 15.4cm$

$= > 11.2cm$

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