Triangle MPT with bar(NR) || bar(MT) is shown below. The dimensions are in centimeters.12210107121.jpgWhich measurement is closest to the length of bar(RT) in centimeters?1)1.42)1.83)3.44)4.3

ankarskogC 2020-11-05 Answered

Triangle MPT with NRMT is shown below. The dimensions are in centimeters.
image
Which measurement is closest to the length of RT in centimeters?
1)1.4
2)1.8
3)3.4
4)4.3

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Expert Answer

Roosevelt Houghton
Answered 2020-11-06 Author has 106 answers
Step 1
Given,
MPT with NRMT
PN = 4 cm
PR = 2.5 cm
NM = 2.9 cm
We have to find the length of RT in centimeters.
Step 2
We have
NRMT
Then, using the properties for two parallel lines cut by transversal lines
PNR=PMT ..........(1)
PRN=PTM ............(2)
Now,
In NPRandMPT
PNR=PMT (from (1))
PRN=PTM (from (2))
NPR=MPT (common angle )
So,
From AAA (angle-angle-angle) rule of similarity
NPRMPT
Step 3
Now,
In similar triangle, ratio of corresponding sides will be equal.
NPMP=PRPT=NRMT
Taking
NPMP=PRPT
4MN+NP=2.5PR+RT (substituted the values)
42.9+4=2.52.5+RT
46.9=2.52.5+RT
4(2.5+RT)=6.9×2.5
4RT+10=17.25
4RT=17.2510
4RT=7.25
RT=7.254
RT=1.8125
So,
The lenght of RT = 1.8cm
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