JAMB Mathematics 2023 Paper

Concept:Use the area of a rectangle and the given increase in area to form and solve an equation.Explanation:Let the longer side be $x$ cm.Then the shorter side is $(x - 6)$ cm.Original area: $A_1 = x(x - 6) = x^2 - 6x$ cm$^2$.After adding 2 cm to each side, the new sides are $(x + 2)$ cm and $(x - 4)$ cm.New area: $A_2 = (x + 2)(x - 4) = x^2 - 2x - 8$ cm$^2$.The area increases by $68$ cm$^2$, so $A_2 - A_1 = 68$.That gives $(x^2 - 2x - 8) - (x^2 - 6x) = 68$.Simplifying: $4x - 8 = 68$, so $4x = 76$.Therefore, $x = 19$ cm.Length of the shorter side: $19 - 6 = 13$ cm.Answer:$13$ cm (Option C).