Some one please help me this question.

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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)

= , substitute values

= ( 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

= , substitute values

= , that is

= ( 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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)