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Mathematics

Grade9

Easy

Question

Find BU.

3
6
9
12

hint 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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