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.
Explanation
(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