2018 WAEC Mathematics Theory In the diagram. PQR is an isosceles triangle. If the perimeter of the triangle is...

In the diagram. PQR is an isosceles triangle. If the perimeter of the triangle is 28 cm, find the:

a. values of x and y;

b. lengths of the sides of the triangle.

(a) By summing 2y + x + 6y - 2x + 1 + 4y = 28 and simplified to arrive at 12y - x = 27 ...............(1).

Similarly, IPRI = IRQI, 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(\(\frac{1}{2}\)). Then, x = 12(\(\frac{5}{2}\)) - 27 = 30 - 27 = 3

(b) The lengths of the sides of the triangle were also obtained as |PO| = 2y + x = 2(\(\frac{5}{2}\)) + 3 = 8 cm.

|QR| = 4y = 4(\(\frac{5}{2}\)) = 10 cm and IPRI = 6y - 2x + 1 = 6(\(\frac{5}{2}\)) - 2(3) + 1 = 10 cm

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