Pleade help and show work

9514 1404 393

  11) x = 9

  12) x = 9

Step-by-step explanation:

11) Corresponding segments are proportional, so ...

  x/6 = 12/8

  x = 6(12)/8 . . . multiply by 6

  x = 9

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12) Similar triangle relationships show you the geometric mean relationship that applies in this case.

  long side/short side = x/3 = 27/x

  x² = 3·27 . . . . . . cross multiply

  x = √(3·27) . . . . geometric mean relationship

  x = 9

They are similar by the Side-Side-Side Theorem. 

The smaller triangle is 3/4 of the second triangle:
90/120; divide each by 10, = 9 / 12 which simplifies to 3/4

135/180; divide each by 15, = 9 / 12 which simplifies to 3/4

117/156; divide each by 13, = 9 / 12 which simplifies to 3/4