Question

A 10 metres long rope is to be cut into two 2 pieces and a square is to be made using each. The difference in the areas enclosed must be 1 1/4 square metres. How should it be cut?

Note:The question is to find the lengths in which 10 cm is cut.​

Answer 1

Given that, a long rope of 10 m is cut in 2 piece,

Enclosed area is $1\frac{1}{4}$

As we have to find the at which size the rope is divided,

Let,

Length of one piece $=x m$

Length of other piece $=(10-x) m$

Агеаs,

$\left(\frac{x}{4}\right)^{2},\left(\frac{10-x}{4}\right)^{2}$

So,

$\left(\frac{x}{4}\right)^{2},\left(\frac{10-x}{4}\right)^{2}=1 \frac{1}{4}$

$\begin{array}{l}=\frac{x^{2}}{16}-\frac{\left(100-20 x+x^{2}\right)}{16}\\\\=1 \frac{1}{4} \\\\=\frac{x^{2}}{16}-\frac{100}{16}+\frac{20 x}{16}-\frac{x^{2}}{16}\\\\=\frac{5}{4}\end{array}$

Now,

$\frac{20x-100}{16} =\frac{5}{4}$

$20x-100=\frac{5*16}{4}$

$20x-100=20;20x=120$

$x=\frac{120}{20}$

$x=6$

Therefore,

Rope is divided into $6 \mathrm{~m}$ and $4 \mathrm{~m}$.