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In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE . If 10AB, 16BC , and 13AD then find the length of AE ?

In the diagram shown points B and D lie on sides AC and AE such that BD is parallel to CE If 10AB 16BC and 13AD then find the length of AE class=

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Nayefx

Answer:

[tex] \displaystyle \overline{AE} = 33.8[/tex]

Step-by-step explanation:

By triangle similarity theorem we acquire:

[tex] \displaystyle \frac{10}{16 + 10} = \frac{13}{ AE } [/tex]

since AE=AD+ED substitute:

[tex] \displaystyle \frac{10}{16 + 10} = \frac{13}{ 13 + ED} [/tex]

simplify addition:

[tex] \displaystyle \frac{10}{26} = \frac{13}{ 13 + ED} [/tex]

cross multiplication:

[tex] \displaystyle 10(13 + ED) = 26 \times 13[/tex]

distribute:

[tex] \displaystyle 13 0+ 10ED = 26 \times 13[/tex]

simplify multiplication:

[tex] \displaystyle 13 0+ 10ED =338[/tex]

cancel 130 from both sides:

[tex] \displaystyle10ED =208[/tex]

divide both sides by 10:

[tex] \displaystyle \: ED =20.8[/tex]

so, the measure of side AE=20.8+13=33.8

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