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vladimir1956 [14]
3 years ago
12

Point C ∈ AB , AB = 30m. Point C is 1.5 times farther from point A than from point B. Find AC and CB.

Mathematics
1 answer:
Shtirlitz [24]3 years ago
8 0

let's say that C is "x" units farther from B, that means that CB = x, and therefore AC = 1.5x.


\bf \underset{\leftarrow ~~30~~\to}{\boxed{A}\stackrel{1.5x}{\rule[0.35em]{18em}{0.25pt}}C\stackrel{x}{\rule[0.35em]{10em}{0.25pt}}\boxed{B}}
\\\\\\
AB=AC+CB\implies \stackrel{AB}{30}=\stackrel{AC}{1.5x}+\stackrel{CB}{x}\implies 30=2.5x
\\\\\\
\cfrac{30}{2.5}=x\implies 12=x
\\\\[-0.35em]
~\dotfill\\\\
AC=1.5(12)\implies AC=18~\hspace{8em} CB=x\implies CB=12

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