Answer:
Divide a [tex]5\frac{1}{4}[/tex] inch line into three parts are [tex]\frac{7}{8},\frac{7}{3},\frac{21}{8}[/tex]
Step-by-step explanation:
To find : Divide a [tex]5\frac{1}{4}[/tex] 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 [tex]x=\frac{ap}{a+b+c}[/tex] , [tex]y=\frac{bp}{a+b+c}[/tex] and [tex]z=\frac{cp}{a+b+c}[/tex]
On comparing, [tex]p=5\frac{1}{4}=\frac{21}{4}[/tex]
a=1 , b=2 , c=3
Substituting all the values to determine the three parts,
[tex]x=\frac{ap}{a+b+c}[/tex]
[tex]x=\frac{1(\frac{21}{4})}{1+2+3}[/tex]
[tex]x=\frac{\frac{21}{4}}{6}[/tex]
[tex]x=\frac{21}{4\times 6}[/tex]
[tex]x=\frac{21}{24}[/tex]
[tex]x=\frac{7}{8}[/tex]
[tex]y=\frac{bp}{a+b+c}[/tex]
[tex]y=\frac{2(\frac{21}{4})}{1+2+3}[/tex]
[tex]y=\frac{\frac{21}{2}}{6}[/tex]
[tex]y=\frac{21}{2\times 6}[/tex]
[tex]y=\frac{21}{12}[/tex]
[tex]y=\frac{7}{3}[/tex]
[tex]z=\frac{cp}{a+b+c}[/tex]
[tex]z=\frac{3(\frac{21}{4})}{1+2+3}[/tex]
[tex]z=\frac{\frac{63}{4}}{6}[/tex]
[tex]z=\frac{63}{4\times 6}[/tex]
[tex]z=\frac{63}{24}[/tex]
[tex]z=\frac{21}{8}[/tex]
Therefore, Divide a [tex]5\frac{1}{4}[/tex] inch line into three parts are [tex]\frac{7}{8},\frac{7}{3},\frac{21}{8}[/tex]
