Respuesta :

devishri1977

Answer:

Step-by-step explanation:

ΔADE & ΔABC are similar triangles

[tex]\frac{AD}{AB}=\frac{DE}{BC}\\\\\frac{10+x}{10}=\frac{10}{6}\\[/tex]

Cross multiply,

6*(10+x) = 10*10

6*10 + 6*x = 100

60 + 6x = 100

6x = 100 - 60

6x = 40

x = 40/6

x = 6.67

Answer:

x ≈ 6.67

Step-by-step explanation:

Δ ACB and Δ AED are similar, thus ratios of corresponding sides are equal, that is

[tex]\frac{CB}{ED}[/tex] = [tex]\frac{AB}{AD}[/tex] , substitute values

[tex]\frac{6}{10}[/tex] = [tex]\frac{10}{10+x}[/tex] ( cross- multiply )

6(10 + x) = 100

60 + 6x = 100 ( subtract 60 from both sides )

6x = 40 ( divide both sides by 6 )

x = [tex]\frac{40}{6}[/tex] ≈ 6.67 ( to 2 dec. places )

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