Question 795235
A segment 150 cm long is divided into 3 parts in the ratio 2:3:5. How long is each part?
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Rule:

if A:B:C = D:E:F then

{{{A/(A+B+C)}}}:{{{B/(A+B+C)}}}:{{{C/(A+B+C)}}} = {{{D/(D+E+F)}}}:{{{E/(D+E+F)}}}:{{{F/(D+E+F)}}}

and

{{{A/(A+B+C)}}} = {{{D/(D+E+F)}}}
{{{B/(A+B+C)}}} = {{{E/(D+E+F)}}}
{{{C/(A+B+C)}}} = {{{F/(D+E+F)}}}

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Let A+B+C = 150 where A:B:C = 2:3:5

then

{{{A/(A+B+C)}}}:{{{B/(A+B+C)}}}:{{{C/(A+B+C)}}} = {{{2/(2+3+5)}}}:{{{3/(2+3+5)}}}:{{{5/(2+3+5)}}}


{{{A/150}}}:{{{B/150}}}:{{{C/150}}} = {{{2/10}}}:{{{3/10}}}:{{{5/10}}}

{{{A/150}}} = {{{2/10}}}
{{{B/150}}} = {{{3/10}}}
{{{C/150}}} = {{{5/10}}}

Solve each by cross-multiplying and get A=30 cm, B=45 cm, C=75 cm

Edwin</pre>