3 years ago

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

_____

Additional comment

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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