Question 197183
A  rough  sketch  helps  to  visualize.
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Large  rt  triangle,  square  corner  on  right, height  an  right  is  12,  other  leg,  horizontal, is  x.
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Smaller  triangle  is  drawn  inside  ,  with  height  5.5.,,,horizontal  leg  is  (x-3).
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horizontal  difference  between  heights  is  3
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Problem  is  proportional  triangles,  one  12  height by  (x) leg,,,other  5.5  high,,(x-3)  leg
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12/x = 5.5 / (x-3)
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cross  multiply
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12x -36 =5.5 x
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6.5 x = 36
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x=5.54,,,,lamppost  shadow  lg
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Therefore  Shad's shadow  lg = (x-3) = 2.54
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checking
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12/5.54 = 5.5 /2.54,,,,,ok