(a) Find the number N such that when \(\frac{1}{3}\) of it is added to 8, the result is the same as when \(\frac{1}{2}\) 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 4 cm apart. < DAB = 60°, /AB/ = 8 cm and /BC/ = 5 cm. Measure /DC/.
Explanation
(a) Let the number be N. \(\frac{N}{3} + 8 = 18 - \frac{N}{2}\) \(\frac{N}{3} + \frac{N}{2} = 18 - 8 = 10\) \(\frac{5N}{6} = 10 \implies 5N = 60\) \(N = 12\) (b)
