BECE Mathematics 2015 Paper

Concept:Use Pythagoras theorem: in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.Explanation:The hypotenuse is the longest side, given as $13$ cm.One side is $5$ cm. Let the third side be $x$ cm.Applying Pythagoras theorem:$$x^2 + 5^2 = 13^2$$$$x^2 + 25 = 169$$$$x^2 = 169 - 25$$$$x^2 = 144$$Since $144 = 12^2$, we get:$$x^2 = 12^2$$Therefore, $x = 12$.Answer:The length of the third side is $12$ cm.Correct option: C. $12$ cm.