Question

BC = 4.8 cm, the length of DE = 1.8cm (Enter 1 f true otherwise 0)

Answer 1

Given $\frac{AD}{BD}=3:5$
$\frac{BD}{AD}=\frac{5}{3}$
$\frac{BD}{AD}+1=\frac{5}{3}+1$
$\frac{BD+AD}{AD}=\frac{5+3}{3}$
$\frac{AB}{AD}=\frac{8}{3}$
$\frac{AD}{AB}=\frac{3}{8}$
In $△ADE$ and $△ABC$
$\angle DAE=\angle BAC$ (Common angle)
$\angle ADE=\angle ABC$ (Corresponding angles)
$\angle AED=\angle ACB$ (Corresponding angles)
Thus, $△ADE\sim △ABC$ (AAA rule)
$\frac{AD}{AB}=\frac{DE}{BC}$ (Corresponding sides)
$\frac{3}{8}=\frac{DE}{4.8}$
$DE=\frac{4.8\times 3}{8}$
$DE=1.8$ cm