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Mars2501 [29]
3 years ago
14

Pleasee help mee ;w;

Mathematics
2 answers:
Nuetrik [128]3 years ago
8 0

Answer:

  • x = 13

Step-by-step explanation:

It is assumed PQS and RQS are similar triangles.

<u>The ratio of corresponding sides is equal:</u>

  • PS/RS = PQ/RQ

<u>Substitute side lengths and solve for x:</u>

  • 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
Xelga [282]3 years ago
5 0

The ratio of sides remains same

\\ \sf\longmapsto \dfrac{PQ}{QS}=\dfrac{RQ}{RS}

\\ \sf\longmapsto \dfrac{21}{15}=\dfrac{5x-16}{3x-4}

\\ \sf\longmapsto \dfrac{7}{5}=\dfrac{5x-16}{3x-4}

\\ \sf\longmapsto 7(3x-4)=5(5x-16)

\\ \sf\longmapsto 21x-28=25x-80

\\ \sf\longmapsto 80-28=25x-21x

\\ \sf\longmapsto 4x=52

\\ \sf\longmapsto x=13

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