Question

A 224 cm rope is cut so that one part is 3/4 of the other. How long is the shorter rope? The longer rope?

Answer 1

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
`(3)/(4)x`.

Total length
`=x+(3)/(4)x`

Now,

`x+(3)/(4)x=224`

`(4x+3x)/(4)=224`

Multiply both sides by 4.

`7x=896`

Divide both sides by 7.

`x=(896)/(7)`

`x=128`

The value of one part 128 cm.

Second part
`=(3)/(4)x`

`=(3)/(4)* 128`

`=3* 32`

`=96`

Therefore, the length of shorter rope is 96 cm and the length of longer rope is 128 cm.