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

Question

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

Roosevelt Houghton · Accepted Answer

Step 1  Given,  △MPT  with NR―∣∣MT―  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   NR―∣∣MT―    Then, using the properties for two parallel lines cut by transversal lines  ∠PNR=∠PMT                        ..........(1)                 ∠PRN=∠PTM                       ............(2)  Now,  In  △NPRand△MPT   ∠PNR=∠PMT                          (from (1))   ∠PRN=∠PTM                         (from (2))  ∠NPR=∠MPT                       (common angle )    So,  From  AAA (angle-angle-angle) rule of similarity   △NPR∼△MPT     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=17.25−10  ⇒4RT=7.25  ⇒RT=7.254  ⇒RT=1.8125  So,  The lenght of RT = 1.8cm

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

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