Question

geometry. find RN. pls help!!

Answer 1

Apply Thales theorem

$\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}$

$\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}$

$\\ \rm\rightarrowtail 8RN=50$

$\\ \rm\rightarrowtail RN=50/8$

$\\ \rm\rightarrowtail RN=6.25$

Answer 2

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)

⇒ $\sf\dfrac{8}{13}=\dfrac{10}{10+RN}$

Cross multiply and solve:

⇒ 8(10 + RN) = 10 × 13

⇒ 80 + 8RN = 130

⇒ 8RN = 130 - 80

⇒ 8RN = 50

⇒ RN = 50 ÷ 8

⇒ RN = 6.25