Question

AABC and ADEF are equilateral triangles, A(AABC): (ADEF) = 1:2
If AB = 4 then what is length of DE = ?
(a)
$2 \sqrt{2}$

(b) 4
(c) 8
d)
$4 \sqrt{2}$
plz give explanation ​

Answer 1

answer: ∆abc and ∆DEF

1:2

ar ∆abc/ ar ∆def = 1/2= (ab)2 /(de)2

1/2= (4)2/(de)2

1/2= 16/(de)2

(de)2=32

DE= √32

de=4√2