Question

A 10 metre long rope is to be cut into two pieces and a square is to be made using each. The difference in the areas enclosed must be 1\(\frac14\) square metres. How should it be cut?

Answer 1

Length of one piece = x m

Length of other piece = (10 – x) m

Areas \((\frac{x}{4})^2,(\frac{10\,-\,x}{4})^2\)

Given that, \((\frac{x}{4})^2,(\frac{10\,-\,x}{4})^2=1\frac{1}{4}\)

\(\text{x}=\frac{120}{20}=6\)

∴ Rope is divided into 6 m and 4 m.