Mathematics
Grade9
Easy

Question

Find the value of x for two similar triangles.

  1. 9    
  2. 11    
  3. 21    
  4. 31    

Hint:

If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles. Find value of x by equating the ratios.

The correct answer is: 9


    If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles.
    fraction numerator E F over denominator A B end fraction equals fraction numerator D E over denominator C B end fraction (Corresponding sides are proportional)
    fraction numerator 21 over denominator 77 end fraction equals fraction numerator 30 over denominator 11 x plus 11 end fraction
    21 left parenthesis 11 x plus 11 right parenthesis blank equals 77 cross times 30
    x equals 9
    Therefore, value of x is 9.

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