QUESTION 4
In the diagram, PQR is an isosceles triangle. If the perimeter of the triangle is 28 cm, find the:
- values of x and y;
- lengths of the sides of the triangle.
Observation
The Chief Examiner reported that this question was popular among the Candidates and majority performed very well.
In part (a), they did as expected by summing 2y + x + 6y – 2x + 1 + 4y = 28 and simplified to arrive at 12y – x = 27 ------------------------------(1).
Similarly, |PR| = |RQ|, which implied that 4y = 6y – 2x + 1. This simplified to
2y – 2x = –1 -----------------------------------(2)
Solving equations (1) and (2) simultaneously gave 2y – 2(12y – 27) = –1, so that y = 2(1/2).
Then, x = 12(5/2)- 27 = 30 – 27 = 3
In part (b), the lengths of the sides of the triangle were also obtained as
|PQ| = 2y + x = 2(5/2) + 3 = 8 cm,
|QR| = 4y = 4(5/2) = 10 cm and |PR| = 6y – 2x + 1 = 6(5/2)-2(3)+1 = 10 cm.