Respuesta :

msm555

Answer:

we have:

∆BDE is similar to ∆BAC

so their side are proportional :

BD/BD=BE/BC

2/BD=4/(6+4)

BD=2×10/4

BD=5

again

BE/BC=DE/AC

4/10=5/AC

AC=5×10/4

AC=25/2

Now,

AC=25/2 or 12.5.

AD=BA-BD=5-2=3.

is your answer.

Answer:

AC = 12.5, AD = 3

Step-by-step explanation:

A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is

[tex]\frac{BD}{BE}[/tex] = [tex]\frac{AD}{CE}[/tex] , substitute values

[tex]\frac{2}{4}[/tex] = [tex]\frac{AD}{6}[/tex] ( cross- multiply )

4 AD = 12 ( divide both sides by 4 )

AD = 3

-----------------------------------------

Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is

[tex]\frac{DE}{AC}[/tex] = [tex]\frac{BD}{BA}[/tex] , substitute values

[tex]\frac{5}{AC}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )

2 AC = 25 ( divide oth sides by 2 )

AC = 12.5

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