(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) Us...
Question 1 Report
(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/.
Answer Details
(a) Let the number be \(N\).
\[\frac{N}{3}+8=18-\frac{N}{2}\]
\[\frac{N}{3}+\frac{N}{2}=18-8\]
\[\frac{5N}{6}=10\]
\[5N=60\]
\[\boxed{N=12}\]
(b) Construction of trapezium \(ABCD\)
- Draw \(AB=8\text{ cm}\).
- At \(A\), construct \(\angle DAB=60^\circ\), and draw the ray \(AD\).
- Construct a perpendicular to \(AB\) at \(A\). Mark a point \(4\text{ cm}\) from \(A\) on this perpendicular and draw through it a line parallel to \(AB\). This line meets the \(60^\circ\) ray at \(D\).
- With centre \(B\) and radius \(5\text{ cm}\), draw an arc to cut the parallel line at \(C\), taking the intersection to the left of \(B\).
- Join \(BC\) and \(DC\).
From the completed construction,
\[\boxed{DC\approx 2.7\text{ cm}}\]
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