CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1 · Question Q45

If a rope of length k\text{ metres} forms three sides of a rectangle of width x\text{ metres} then the area, R, in square metres, of the rectangle is given by R = x(k - 2x). The MAXIMUM value of R is

1. (A)\frac{k^2}{8}
2. (B)\frac{k^2}{4}
3. (C)\frac{k}{16}
4. (D)\frac{k}{4}