Question

If $\triangle ABC and \triangle DEF$ are similar such that 2AB = DE and BC = 8 cm, then EF =
(a) 16 cm
(b) 12 cm
(c) 8 cm
(d) 4 cm

Answer 1

Answer:

The length of EF is 16 cm.

Among the given options option (a) is 16 cm is the correct answer.

Step-by-step explanation:

Given:

ΔABC and  ΔDEF are similar  

ΔABC ~ ΔDEF  

DE = 2 AB

BC = 8 cm

 

DE = 2 AB

AB/DE = ½  

 

AB/DE = BC/EF = CA/FD

[corresponding sides of two similar triangles are in proportional]

AB/DE = BC/EF

½ = 8/EF

EF = 2 × 8  

EF = 16 cm

Hence, the length of EF is 16 cm.

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Answer 2

$\huge\underline\mathfrak\red{Answer:-}$

Length of EF=16 cms.

$\huge\mathfrak{Solution:-}$

=>Triangle ABC and DEF are similar

and DE = 2AB and BC = 8 cm

⭐Then according to sides theorem :-

AB / DE = BC / EF

----> AB / 2AB = BC / EF  [as DE = 2AB]

----> 1 / 2 = BC / EF

----> EF = 2BC

----> EF = 2 × 8 = 16 cm.