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Mathematics : asked on vixen0528ow6mza
 30.04.2023

Triangle LMN is similar to triangle MNP. 16.0 in. M 8.0 in. Part A What is the length of NP in inches? Enter your answer in the box, Part B If the perimeter of triangle LMN is 43.2 inches, what is the perimeter of triangle MNP in inches?

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11.02.2022, solved by verified expert
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Ranjana Bhatt
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Triangle LMN ~ Triangle MNP

Therefore LM/MN = MN/NP = LN/MP ....................(1)  (ratio of corresponding sides of similar triangles)

16/8 = 8/NP

2 = 8/NP

NP = 8/2 = 2 

NP is 2 inches. 

The perimeter of LMN = 43.2 inches 

LM + MN + LN =43.2

16 + 8 + LN= 43.2

LN = 43.2 - 24 = 19.2

from eq. (1)

16/8 = 19.2/MP

2 = 19.2/MP

MP = 19.2/2 = 9.6 inches 

Perimeter of triangle MNP =

MN + NP + MP 

= 8 +2 +9.6 = 19.6 inches 

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