Respuesta :

Answer:

AB = 3 and AC = 4

Step-by-step explanation:

Given that the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AB}{WX}[/tex] = [tex]\frac{BC}{WY}[/tex] , substitute values

[tex]\frac{AB}{30}[/tex] = [tex]\frac{3}{30}[/tex] ( cross- multiply )

30AB = 90 ( divide both sides by 30 )

AB = 3

and

[tex]\frac{AC}{XY}[/tex] = [tex]\frac{BC}{WY}[/tex] , substitute values

[tex]\frac{AC}{40}[/tex] = [tex]\frac{3}{30}[/tex] ( cross- multiply )

30AC = 120 ( divide both sides by 30 )

AC = 4

absor201

Answer:

  • AB = 3
  • AC = 4

Step-by-step explanation:

  • Let AB = x
  • Let AC = y

Given

ΔWXY ~ ΔBAC

Therefore, the triangles are similar, so corresponding sides would be in the same ratio, so

WY/ BC = XW/AB

substitute WY = 30, BC = 3, XW = 30, AB = x

30 / 3 = 30 / x

x = [30 × 3] / [30]

x = 90 / 30

x = 3

Thus,

AB = 3

now

WY/ BC = XY/AC

substitute WY = 30, BC = 3, XY = 40, AC = y

30 / 3 = 40 / y

y = [40 × 3] / [30]

y = 120 / 30

y = 4

Thus,

AC = 4

Therefore,

  • AB = 3
  • AC = 4

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