Question

Triangles LMN and NWR are right triangles. What is

Answer 1

Answer:

NW = 15.6 cm

Step-by-step explanation:

If ΔLMN ~ ΔNWR then:

$\sf LN : LM = RN : RW$

$\implies \sf \dfrac{LN}{LM}=\dfrac{RN}{RW}$

$\implies \sf \dfrac{10}{24}=\dfrac{6}{RW}$

$\implies \sf 10RW=6 \cdot 24$

$\implies \sf RW = 14.4\:cm$

Find NW by using Pythagoras' Theorem:

$a^2+b^2=c^2$

(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:

$\implies \sf 6^2+14.4^2=NW^2$

$\implies \sf NW^2=243.36$

$\implies \sf NW=\sqrt{243.36}$

$\implies \sf NW=15.6\:cm$

Answer 2

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