Suppose ABCDE is similar LMNPQ and that AB = 12, CE = 18, BE = 15, PQ = 24, and LM = 20. Also suppose that AB + DE = CD. Find NQ, MQ, DE, and NP.

Answer 1

1) Because these two figures are "similar," their measurements will be proportional. Therefore:

AB ~ LM

BC ~ MN

CD ~ NP

DE ~ PQ

CE ~ NQ

BE ~ MQ

2) If AB = 12 and LM =20, then you will need to set up a proportion to find the missing sides.

12 = DE

20 24 PQ = 24 SOLVE: 12*24 = 20DE

288 = 20 DE

DE = 14.4

3) Now, find CD with the equation provided in the question: AB + DE = CD

12 + 14.4 = 26.4 CD = 26.4

4) The reason you need to find CD is to help you set up the proportion for NP

12 = 26.4

20 NP SOLVE: 12NP = 26.4*20

12NP = 528

NP = 44

5) Solve for NQ using a proportion:

12 = 18

20 NQ SOLVE: 12NQ = 18*20

12NQ = 360

NQ = 30

6) Solve for MQ using a proportion:

12 = 15

20 MQ SOLVE: 12MQ = 15*20

12MQ = 300

MQ = 25

To check, make sure all of the equivalent sides of LMNPQ are larger than the ABCDE counterparts.