Question

The area of a trapezium is 847 cm2. If the ratio of parallel sides is 9:2
and the distance between them is 14 cm, find the length of the parallel
sides

Answer 1

$\textbf{\huge{Answer}} \: \: \\ \\ area \: of \: trapezium = 847 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ distance \: between \: paralell \: sides \: = 9 \colon 2 \\ height = 14 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {\underline{\underline{\boxed{\sf{area \: of \: trapezium = \frac{1}{2} \times (distance \: between \: paralell \: sides) \times height }}}}} \\ \\ 847 = \: \frac{1}{2} \times (9x + 2x) \times 14 \: \: \: \: \: \\ \\847 = \: \frac{1}{2} \times 11x \times 14 \: \: \: \: \: \: \: \: \: \: \\ \\ 847 = 7 \times 11x \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ 847 = 77x \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x = \frac{847}{77} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x = 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ distance \: between \: the \: paralell \: sides \: are \: 9x \colon2x = 99\colon22$