Question

find the lenghts of the parallel sides of a trapezuim, if the area is 720 cm^2 and the ratio of its parallel sides is 2:3 where the distance between them is 72 cm

Answer 1

$\\ \\ \color{blue} \underline{ \large\sf \: Question :-}$

find the lenghts of the parallel sides of a trapezuim, if the area is 720 cm^2 and the ratio of its parallel sides is 2:3 where the distance between them is 72 cm.

$\\ \\ \color{blue} \underline{ \large\sf \: Solution :-}$

$\\ \\ \: \: \: \: \: \: \: \sf \: Let \: the \: length \: of \: parallel \: sides \: be \: 2x \: and \: 3x \: respectively.$

$\\ \\ \sf \: We \: know \: that,$

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

$\\ \\ \sf \: Here, \: h \: is \: height \: and \: a \: is \: a \: length \: o f \: side \: \\ \sf \: which \: are \: parallel \: to \: another \: side \: which \: i s \: b .$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: Now, \: put \: the \: given \: values \: in \: f ormula$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies720 \: = \: \frac{1}{2} \times 72(2x + 3x)$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies720 \: = \: \frac{1}{2} \times 72 \times 5x$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies720 \: = \: 36 \times 5x$

$\\ \\ \sf \: \therefore\: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 5x \: = \: \frac {720}{36}$

$\\ \\ \sf \: \therefore\: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 5x \: = \: 20$

$\\ \\ \sf \: \therefore\: \: \: \: \: \: \: \: \: \: \: \: : \implies \: x \: = \frac{20}{5}$

$\\ \\ \sf \: \therefore\: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \underline {\boxed{ \orange{ \tt x \: = 4}}}$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Now , \: put \: the \: value \: o f \: x \: in \:given \: sides$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \therefore \: (1): \: 2x = 2 \times 4 = 6cm$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \therefore \: (2): \: 3x = 3 \times 4 = 12cm$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \underline{ \sf \: hence ,\: The \: lenghts \: of \: the \: parallel \: sides \: of \: a \: trapezuim \: is \: 6 \: cm \: and \: 12 \: cm \: respectively. }$