Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

geometry. find RN. pls help!!

Geometry Find RN Pls Help class=

Sagot :

Apply Thales theorem

[tex]\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}[/tex]

[tex]\\ \rm\rightarrowtail 8RN=50[/tex]

[tex]\\ \rm\rightarrowtail RN=50/8[/tex]

[tex]\\ \rm\rightarrowtail RN=6.25[/tex]

semsee45

Answer:

RN = 6.25

Step-by-step explanation:

Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Therefore,

MQ : MP = MR : MN

⇒ 8 : (8 + 5) = 10 : (10 + RN)

⇒ 8 : 13 = 10 : (10 + RN)

⇒ [tex]\sf\dfrac{8}{13}=\dfrac{10}{10+RN}[/tex]

Cross multiply and solve:

⇒ 8(10 + RN) = 10 × 13

⇒ 80 + 8RN = 130

⇒ 8RN = 130 - 80

⇒ 8RN = 50

⇒ RN = 50 ÷ 8

⇒ RN = 6.25

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.