HKDSE MATHEMATICS

Inthe question, "If its length by 3 cm ......" should be "If itslength is increased by 3 cm".

Let y cm be the length of the rectangle.
Then, the width of the rectangle = (66 - 2a)/2 cm = (33 - a) cm

(New area) = (14/15) x (Original area)
(y + 3)[(33 - y) - 3] = (14/15)y(33 - y)
15(y + 3)(30 - y) = 14y(33 - y)
15(y + 3)(y - 30) = 14y(y - 33)
15y² - 405y - 1350 = 14y² - 462y
y² + 57y - 1350 = 0
(y - 18)(y + 75) = 0
y = 18 or y = -75 (rejected for length must be positive)
33 - y = 15

The dimensions of the rectangle: 18cm x 15 cm