2008 - WAEC Mathematics Past Questions and Answers - page 5

Perimeter of (\bigtriangleup) PQR = PQ + QR + PR

24cm = 6cm + 8cm = PR

24 = 14 + PR

PR = 24 - 14 = 10cm

Area of (\bigtriangleup) PRS = (\frac{1}{2} \times 10 \times 3cm^3)

= 15cm³

(\bigtriangleup) RST is equilateral triangle, hence

< TRS = < RTS = < RSt = 60^o

But < PTR = 60^o(Angle between a chord and a tangent at the point of contact = Angle in the alt. segment). From the diagram < PTS = < PTR + < RTS

= 60^o + 60^o = 120^o

< RQT = < QRS = 2x (Alternate angles). But in (\bigtriangleup) PRQ

50 + 60 + (2x + 3x) = 180^o(Angles in a triangle)

110 + 5x = 180^o

5x = 180^o - 110 = 70^o

x = (\frac{70}{5}) = 14^o

Also y + 50 + 2(14) = 180^o

y + 50 + 28 = 180^o

y = 180 - 78

y = 102^o

2 x s = 280°(Angle at centre = 2 x < at circum)

S = \(\frac{280^o}{2}\)

= 140°

< O = 360 - 280 = 80°

60 + 80 + 140 + a = 360°

(< in a quad); 280 + a = 360

a = 360 - 280

a = 80°

M = Mercedez; T = Toyota

Number of staff = 0 + (20 - 5) + (15 - 5) + 5

0 + 15 + 10 + 5 = 30