Respuesta :

Find RW then use Pythagorean theorem

  • ML/LN=RW/NR
  • 24/10=RW/6
  • 12/5=RW/6
  • 5RW=72
  • RW=14.4

So

  • NW²=RW²+NR²=6²+14.4²=36+201.6=237.6
  • NW=√237.6
  • NW=15.5cm
semsee45

Answer:

NW = 15.6 cm

Step-by-step explanation:

If ΔLMN ~ ΔNWR then:

[tex]\sf LN : LM = RN : RW[/tex]

[tex]\implies \sf \dfrac{LN}{LM}=\dfrac{RN}{RW}[/tex]

[tex]\implies \sf \dfrac{10}{24}=\dfrac{6}{RW}[/tex]

[tex]\implies \sf 10RW=6 \cdot 24[/tex]

[tex]\implies \sf RW = 14.4\:cm[/tex]

Find NW by using Pythagoras' Theorem:

[tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

  • a = RN = 6 cm
  • b = RW = 14.4 cm
  • c = NW

Substituting the given values into the formula and solving for NW:

[tex]\implies \sf 6^2+14.4^2=NW^2[/tex]

[tex]\implies \sf NW^2=243.36[/tex]

[tex]\implies \sf NW=\sqrt{243.36}[/tex]

[tex]\implies \sf NW=15.6\:cm[/tex]

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