Theory question 108
Linear and Simultaneous Equations(a) Find the number N such that when 1/3 of it is added to 8, the result is the same as when ½ of it is subtracted from 18. (b) Using a ruler and a pair of compasses only construct a trapezium ABCD, in which the parallel sides AB and DC are 4cm apart. <DAB = 60°, /AB/ = 8cm and /BC/ = 5cm. Measure /DC/.
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(a) N/3 + 8 = 18 − N/2. Multiply by 6: 2N + 48 = 108 − 3N, so 5N = 60 and N = 12.
(b) Draw AB = 8 cm. Construct 60° at A. Construct a line parallel to AB, 4 cm from it (e.g. erect a perpendicular at A or B, mark 4 cm, and draw the parallel through that point). D is where the 60° arm meets the parallel line.
With centre B and radius 5 cm, cut the parallel line at C (on the same side as D, so that ABCD is a trapezium with DC between the 60° arm and B's arc).
Join BC. Construction lines and arcs must be shown.
/DC/ ≈ 2.7 cm (accept 2.6 – 2.8 cm).
AD = 4/sin 60° ≈ 4.6 cm and C is 3 cm horizontally from B, so DC ≈ 8 − 2.3 − 3 = 2.7 cm; use this to check your drawing.