itsvanessalopez itsvanessalopez
  • 14-01-2021
  • Mathematics
contestada

Find the value of x.
B
X+5
4
D
E
2x
3
А
x = [?]

Find the value of x B X5 4 D E 2x 3 А x class=

Respuesta :

jimrgrant1 jimrgrant1
  • 14-01-2021

Answer:

x = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar triangles, thus the ratio of corresponding sides are equal, that is

[tex]\frac{BD}{BA}[/tex] = [tex]\frac{BE}{BC}[/tex], substitute values

[tex]\frac{x+5}{3x+5}[/tex] = [tex]\frac{4}{7}[/tex] ( cross- multiply )

4(3x + 5) = 7(x + 5) ← distribute parenthesis on both sides )

12x + 20 = 7x + 35 ( subtract 7x from both sides )

5x + 20 = 35 ( subtract 20 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

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