QUESTION 3
A garden, in the form of a square, is surrounded by a path which is 1 m wide on two opposite sides and ½ m wide on the other two opposite sides. If the area of the path is 17 m2, calculate the:
(a) perimeter of the garden;
(b) area of the space covered by the garden and the path.
Observation
The Chief Examiner reported this question was also popular among the candidates. According to the report, candidates’ performance was fair.
Candidates were expected to illustrate the given problem in a diagram such
as
From the diagram, the area of garden + path = (x + 2)(x + 1) m2. Area of the garden = x2 m2. From the second statement, (x + 2)(x + 1) – x2 = 17. Solving this equation gave x = 5 m. Therefore, perimeter of garden = 5 × 4 = 20 m2. Area of space covered by garden and path = (5 + 2)(5 + 1) = 42 m2.