The area of a trapezium is 200 cm\(^2\). Its parallel sides are in the ratio

Explanation

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 ÷ \(\frac{5}{3} = 25\times\frac{3}{5} = 15cm\)

From equation (ii)

⇒ a = \(\frac{2 \times 15}{3} = 2\times5 = 10cm\)

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