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 $\dfrac{3}{4}x$.

Total length $=x+\dfrac{3}{4}x$

Now,

$x+\dfrac{3}{4}x=224$

$\dfrac{4x+3x}{4}=224$

Multiply both sides by 4.

$7x=896$

Divide both sides by 7.

$x=\dfrac{896}{7}$

$x=128$

The value of one part 128 cm.

Second part $=\dfrac{3}{4}x$

$=\dfrac{3}{4}\times 128$

$=3\times 32$

$=96$

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