Answer:
x = -0.25
Explanation:
You want to solve for x when corresponding sides of the similar triangles have lengths 6 and 15, and (2x -3) and (3x -8).
Proportion
Corresponding sides are proportional in similar triangles, so we have ...
(2x -3)/6 = (3x -8)/15
5(2x -3) = 2(3x -8) . . . . . . multiply by 30
10x -15 = 6x -16 . . . . . . simplify
4x = -1 . . . . . . . . . . . . add 15-6x
x = -0.25
The value of x is -0.25.
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Additional comment
This negative value of x gives side length ratios in the two triangles of -7/12. Negative side lengths of -3.50 and -8.75 make no sense geometrically. The proportion is satisfied, but the figure cannot be drawn with a negative side length.
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