If MR = 5(a + 6) and MP = 12a + 32, find MR, RP, and MP.

Question

MNPQ is a parallelogram with diagonals QN

 and MP.

If MR = 5(a + 6) and MP = 12a + 32,  find MR, RP, and MP.

Answer 1

Diagonals of a parallelogram bisect each other (MR = RP), so MR is one half of MP.

MR = MP/2

substituting expressions given for MR and MP:

5(a+6) = (12a + 32)/2

10(a+6) = 12a + 32

10a + 60 = 12a + 32

28 = 2a

14 = a

MR = 5(a+6) = 5(14+6) = 100

RP = MR = 100

MP = 12a + 32 = 12(14) + 32 = 200 (which is MR + RP)

Answer 2

MR=RP

MP=MR+RP

12a+32=10(a+6)

12a+32=10a+60

2a = 28

a=14

substitute