Given that:
Length of a rope = 224 cm
Rope is cut so that one part is 3/4 of the other.
Solution:
Let one part of a rope be x cm.
So other part of the rope is [tex]\dfrac{3}{4}x[/tex].
Total length [tex]=x+\dfrac{3}{4}x[/tex]
Now,
[tex]x+\dfrac{3}{4}x=224[/tex]
[tex]\dfrac{4x+3x}{4}=224[/tex]
Multiply both sides by 4.
[tex]7x=896[/tex]
Divide both sides by 7.
[tex]x=\dfrac{896}{7}[/tex]
[tex]x=128[/tex]
The value of one part 128 cm.
Second part [tex]=\dfrac{3}{4}x[/tex]
[tex]=\dfrac{3}{4}\times 128[/tex]
[tex]=3\times 32[/tex]
[tex]=96[/tex]
Therefore, the length of shorter rope is 96 cm and the length of longer rope is 128 cm.
