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The value of x in the given set triangles are:
1) x=17.5
2) x=48
3) x= 8
4) 24.5
5) x=11
6) x=9
What is Triangle Proportionality Theorem?
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides.
1) According to Triangle Proportionality Theorem,
from given fig 1,
[tex]\frac{14}{12} =\frac{x}{15} \\\\\frac{7}{6} =\frac{x}{15} \\\\x= 17.5[/tex]
2) From fig 2,
[tex]\frac{x}{18} =\frac{56}{21} \\\\x=48[/tex]
3) From fig 3,
[tex]\frac{x}{36} =\frac{10}{45} \\\\\frac{x}{36} =\frac{2}{9} \\\\x=8[/tex]
4) From fig 4,
[tex]\frac{6}{21}=\frac{7}{x} \\\\6x=7*21\\\\x=24.5[/tex]
5) From fig 5,
[tex]\frac{30}{x+7} =\frac{25}{15} \\\\\frac{30}{x+7} =\frac{5}{3} \\\\x=11[/tex]
6) From fig 6,
[tex]\frac{6}{21}=\frac{x-1}{3x+1} \\\\ 18xx+6=21x-21\\\\3x=27\\\\x=9[/tex]
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