Mathematics
Grade9
Easy

Question

AB = x + 5, BD = 12, AC = 3x + 1, and CF = 15. Find the value of x if ABC is a triangle and BC ll DF.

  1. x= 3
  2. x=6
  3. x=9
  4. x=12

hintHint:

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

The correct answer is: x=6


    fraction numerator A B over denominator B D end fraction equals fraction numerator A C over denominator C F end fraction left parenthesis T r i a n g l e space P r o p o r t i o n a l i t y space T h e o r e m right parenthesis
fraction numerator left parenthesis x plus 5 right parenthesis over denominator 12 end fraction equals fraction numerator 3 x plus 1 over denominator 15 end fraction
15 left parenthesis x plus 5 right parenthesis equals 12 left parenthesis 3 x plus 1 right parenthesis
15 x plus 75 equals 36 x space plus 12
75 minus 12 equals 36 x minus 15 x
63 equals space 21 x
X equals 63 over 21 equals 3
    Hence, the correct option is A.

    It is also called basic proportionality theorem.

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