Mathematics
Grade9
Easy

Question

Find BU.

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

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.

The correct answer is: 9


    BY similarity, ΔSUT ~ ΔBUC
    fraction numerator T U over denominator S U end fraction equals fraction numerator T C over denominator S B end fraction
    TU = TC + CU = 18 + 6 (from diagram)
    let SB be x then ,
    fraction numerator 18 plus 6 over denominator 12 end fraction equals fraction numerator 18 over denominator x end fraction
    fraction numerator 24 over denominator 12 end fraction equals fraction numerator 18 over denominator x end fraction
    2 x equals 18
    x equals 9
    SB = 9 then BU = SU - SB = 12 -9 = 3
    Therefore, Value of side BU is 3.

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