BECE Mathematics 2012 Paper

Concept:Use Pythagoras theorem for a right-angled triangle: the square of the hypotenuse equals the sum of the squares of the other two sides.Explanation:In triangle $ABC$, the right angle is at $B$.Therefore, $AC$ is the hypotenuse, and the two shorter sides are $AB = 3$ cm and $BC = 4$ cm.By Pythagoras theorem:$$AC^2 = AB^2 + BC^2$$Substitute the given lengths:$$AC^2 = 3^2 + 4^2$$$$AC^2 = 9 + 16$$$$AC^2 = 25$$Since $25 = 5 \times 5$, we get:$$AC^2 = 5^2$$Taking the positive square root:$$AC = 5 \text{ cm}$$Answer:The length of $AC$ is $5$ cm.Correct option: B. 5 cm.