Question

Geometry. find RN. pls help!!

Answer 1

Apply Thales theorem

`\\ \rm\rightarrowtail (MR)/(RN)=(MQ)/(QP)`

`\\ \rm\rightarrowtail (10)/(RN)=(8)/(5)`

`\\ \rm\rightarrowtail 8RN=50`

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

`\\ \rm\rightarrowtail RN=6.25`

Answer 2

RN = 6.25

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(8)/(13)=(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