Question

IF AABC ~ ADEF such that area of ∆ABC is 9cm and the area of ∆ADEF is
16cm and BC = 2.1 cm. Find the length of EF.​

Answer 1

Answer:

2.8cm

Step-by-step explanation:

Triangle ABC ~ Triangle DEF

Therefore,

$\frac{bc}{ef } = \frac{ac}{df } = \frac{ab}{de}$

$area \: \frac{abc}{def} = \frac{16}{9}$

$({ \frac{bc}{ef} }^{2} ) = \frac{16}{9}$

$\frac{ {bc}^{2} }{ef {}^{2} } = \frac{16}{9}$

${ef}^{2} = \frac{16}{9} \times {2.1}^{2}$

$ef = \sqrt{ \frac{16 \times 2.1}{9} }$

$ef \: = \: 2.8 \:cm$

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