Respuesta :

fieryanswererft

Answer:

  • x = 12 units
  • perimeter = 113 units

Given for big triangle:

  • MN = 36
  • MO = 3x + 9 + 15 = 3x + 24

Given for small triangle:

  • side 1 : 36 - 9 = 27
  • side 2 : 3x + 9

setting up proportionality:

[tex]\hookrightarrow \sf \dfrac{36}{3x+24} = \dfrac{27}{3x+9}[/tex]

[tex]\hookrightarrow \sf 36(3x+9) = 27(3x+24)[/tex]

[tex]\hookrightarrow \sf 108x+324 = 81x+648[/tex]

[tex]\hookrightarrow \sf 108x-81x = 648-324[/tex]

[tex]\hookrightarrow \sf 27x = 324[/tex]

[tex]\hookrightarrow \sf x = 12[/tex]

Perimeter of the triangle:

36 + 17 + 15 + 3x + 9

36 + 17 + 15 + 3(12) + 9

113 units

semsee45

Answer:

x = 12

perimeter = 113 units

Step-by-step explanation:

Triangle Proportionality Theorem states that if a line parallel to one side of the triangle intersects the other two sides, then it divides the sides into proportional corresponding segments.

[tex]\implies 3x+9 : 15 = (36-9) : 9[/tex]

[tex]\implies 3x+9 : 15 = 27 : 9[/tex]

[tex]\implies \dfrac{3x+9}{15}= \dfrac{27}{9}[/tex]

[tex]\implies 3x+9 = 45[/tex]

[tex]\implies 3x = 36[/tex]

[tex]\implies x = 12[/tex]

Perimeter = [tex]3x+9 + 15 + 17 + 36[/tex]

Substituting [tex]x = 12[/tex]:

⇒ perimeter = 3(12) + 9 + 15 + 17 + 36

                     = 113

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