Respuesta :

mhanifa

Answer:

  • x = 13

Step-by-step explanation:

It is assumed PQS and RQS are similar triangles.

The ratio of corresponding sides is equal:

  • PS/RS = PQ/RQ

Substitute side lengths and solve for x:

  • 15/(3x - 4) = 21/(5x - 16)
  • 15(5x - 16) = 21(3x - 4)
  • 5(5x - 16) = 7(3x - 4)
  • 25x - 80 = 21x - 28
  • 25x - 21x = 80 - 28
  • 4x = 52
  • x = 52/4
  • x = 13

The ratio of sides remains same

[tex]\\ \sf\longmapsto \dfrac{PQ}{QS}=\dfrac{RQ}{RS}[/tex]

[tex]\\ \sf\longmapsto \dfrac{21}{15}=\dfrac{5x-16}{3x-4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{7}{5}=\dfrac{5x-16}{3x-4}[/tex]

[tex]\\ \sf\longmapsto 7(3x-4)=5(5x-16)[/tex]

[tex]\\ \sf\longmapsto 21x-28=25x-80[/tex]

[tex]\\ \sf\longmapsto 80-28=25x-21x[/tex]

[tex]\\ \sf\longmapsto 4x=52[/tex]

[tex]\\ \sf\longmapsto x=13[/tex]

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