JAMB Mathematics 2023 Paper

Area of trapezium = $\frac{1}{2}(a + b)h$

⇒ $\frac{1}{2} (a + b) \times 16 = 200$

⇒ 8(a + b) = 200

⇒ a + b = $\frac{200}{8}$ = 25 -----(i)

⇒ a : b = 2 : 3

⇒ $\frac{a}{b} = \frac{2}{3}$

⇒ 3a = 2b

⇒ a = $\frac{2b}{3}$ -------(ii)

Substitute $\frac{2b}{3}$ for a in equation (i)

⇒ $\frac{2b}{3}$ + b = 25

$\frac{5b}{3}$ = 25

⇒ b = 25 ÷ $\frac{5}{3} = 25 \times \frac{3}{5} = 15\,\mathrm{cm}$

From equation (ii)

⇒ a = $\frac{2 \times 15}{3} = 2 \times 5 = 10\,\mathrm{cm}$

∴ Lengths of each parallel sides are 10cm and 15cm