Answer:
8.25 cm and 12.5 cm
Step-by-step explanation:
Given a line parallel to a side of the triangle and it intersects the other two sides, then it divides those sides proportionally, that is
(i)
[tex]\frac{AD}{DB}[/tex] = [tex]\frac{AE}{EC}[/tex] , substitute values
[tex]\frac{2.5}{3}[/tex] = [tex]\frac{3.75}{EC}[/tex] ( cross- multiply )
2.5 EC = 11.25 ( divide both sides by 2.5 )
EC = 4.5 cm
Then
AC = AE + EC = 3.75 + 4.5 = 8.25 cm
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(ii)
Similarly
[tex]\frac{AD}{DB}[/tex] = [tex]\frac{AE}{EC}[/tex] , substitute values
[tex]\frac{3.6}{10-3.6}[/tex] = [tex]\frac{4.5}{EC}[/tex] , that is
[tex]\frac{3.6}{6.4}[/tex] = [tex]\frac{4.5}{EC}[/tex] ( cross- multiply )
3.6 EC = 28.8 ( divide both sides by 3.6 )
EC = 8 cm
and
AC = AE + EC = 4.5 + 8 = 12.5 cm
