BECE Mathematics 2022 Paper

Concept:The distances due north and due east form a right-angled triangle, so use Pythagoras’ theorem to find the straight-line distance from the starting point.Explanation:Distance due north = $12\,\mathrm{km}$.Distance due east = $5\,\mathrm{km}$.These two distances are perpendicular to each other.Let $x$ be the shortest distance from the starting point to the final point.By Pythagoras’ theorem:$$x^2 = 12^2 + 5^2$$$$x^2 = 144 + 25$$$$x^2 = 169$$Take the positive square root:$$x = \sqrt{169} = 13\,\mathrm{km}$$Answer:Adjoa was $13\,\mathrm{km}$ away from her starting point.Correct option: C. $13\,\mathrm{km}$.