Answer:
x = 4 and x = 7
Step-by-step explanation:
Given that the segment in the triangle is parallel to the third side of the triangle and intersects the 2 sides then it divides these 2 sides in proportion, thus
[tex]\frac{x}{12}[/tex] = [tex]\frac{x+1}{15}[/tex] ( cross- multiply )
15x = 12(x + 1) ← distribute
15x = 12x + 12 ( subtract 12x from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
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[tex]\frac{8}{7}[/tex] = [tex]\frac{16}{2x}[/tex] ( cross- multiply )
16x = 112 ( divide both sides by 16 )
x = 7