WAEC Mathematics 2018 Paper

Concept:The diagonals of a rhombus bisect each other at right angles, so each side forms the hypotenuse of a right triangle with half-diagonals.Explanation:Let the side of the rhombus be $s$ cm.The diagonals intersect at $M$, so $|MW| = 5$ cm and $|MX| = 12$ cm are half-diagonals.They are perpendicular, so triangle $WMX$ is right-angled at $M$.Using Pythagoras' theorem:$s^2 = 5^2 + 12^2 = 25 + 144 = 169$$s = \sqrt{169} = 13$ cmPerimeter of a rhombus $= 4 \times$ side.Perimeter $= 4 \times 13 = 52$ cm.Answer:The perimeter is $52$ cm, which is option C.