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storchak [24]
3 years ago
11

Proportions in similar triangles. need help

Mathematics
1 answer:
erik [133]3 years ago
6 0

Answer:

  x = 6

Step-by-step explanation:

The angle bisector divides the triangle sides proportionally:

  (6x -1)/42 = (10x +5)/78

  13(6x -1) = 7(10x +5) . . . . multiply by 546 (the LCM of 42 and 78)

  78x -13 = 70x +35 . . . . . eliminate parentheses

  8x = 48 . . . . . . . . . . . . . . add 13-70x

  x = 6 . . . . . . . . . . . divide by 8

_____

<em>Additional comment</em>

The unknown segment lengths are ...

  6·6 -1 = 35

  10·6 +5 = 65

Then the ratios to the known sides are ...

  35/42 = 65/78 = 5/6

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