Question

given DE parallel to BC AD=4.5 BD=9cm EC=8cm what is length of AE​

Answer 1

Basic proportionality theorem(Thales theorem):

If a line is drawn parallel to one side of a triangle then it cuts other two sides proportionally.

By basic proportionality theorem.,

$\frac{AD}{BD}=\frac{AE}{EC}$

$\implies\frac{4.5}{9}=\frac{AE}{8}$

$\implies\frac{1}{2}=\frac{AE}{8}$

$\implies\frac{8}{2}=AE$

$\implies\bf\,AE=4\,cm$