Answer:
Divide a \(5\frac{1}{4}\) inch line into three parts are \(\frac{7}{8},\frac{7}{3},\frac{21}{8}\)
Step-by-step explanation:
To find : Divide a \(5\frac{1}{4}\) inch line into three parts whose ratios are 1:2:3 ?
Solution :
Let the number be p which is divided into three parts in the ratio a : b : c.
then the solution of three parts are \(x=\frac{ap}{a+b+c}\) , \(y=\frac{bp}{a+b+c}\) and \(z=\frac{cp}{a+b+c}\)
On comparing, \(p=5\frac{1}{4}=\frac{21}{4}\)
a=1 , b=2 , c=3
Substituting all the values to determine the three parts,
\(x=\frac{ap}{a+b+c}\)
\(x=\frac{1(\frac{21}{4})}{1+2+3}\)
\(x=\frac{\frac{21}{4}}{6}\)
\(x=\frac{21}{4\times 6}\)
\(x=\frac{21}{24}\)
\(x=\frac{7}{8}\)
\(y=\frac{bp}{a+b+c}\)
\(y=\frac{2(\frac{21}{4})}{1+2+3}\)
\(y=\frac{\frac{21}{2}}{6}\)
\(y=\frac{21}{2\times 6}\)
\(y=\frac{21}{12}\)
\(y=\frac{7}{3}\)
\(z=\frac{cp}{a+b+c}\)
\(z=\frac{3(\frac{21}{4})}{1+2+3}\)
\(z=\frac{\frac{63}{4}}{6}\)
\(z=\frac{63}{4\times 6}\)
\(z=\frac{63}{24}\)
\(z=\frac{21}{8}\)
Therefore, Divide a \(5\frac{1}{4}\) inch line into three parts are \(\frac{7}{8},\frac{7}{3},\frac{21}{8}\)
