Question

# The area of a trapezium is 180 cm2 and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.

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Solution

## $\mathrm{Let}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}x\mathrm{cm}\mathrm{and}\left(x+6\right)\mathrm{cm}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Now},\phantom{\rule{0ex}{0ex}}\mathrm{Area}\mathrm{of}\mathrm{trapezium}=\left\{\frac{1}{2}×\left(x\mathit{+}x\mathit{+}\mathit{6}\right)×9\right\}{\mathrm{cm}}^{2}$ $=\left(\frac{1}{2}×\left(2x+6\right)×9\right){\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}=4.5\left(2x+6\right){\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}=\left(9x+27\right){\mathrm{cm}}^{2}$ $\mathrm{Area}\mathrm{of}\mathrm{trapezium}=180{\mathrm{cm}}^{2}\left(\mathrm{Given}\right)\phantom{\rule{0ex}{0ex}}\therefore 9x+27=180\phantom{\rule{0ex}{0ex}}⇒9x=\left(180-27\right)\phantom{\rule{0ex}{0ex}}⇒9x=153\phantom{\rule{0ex}{0ex}}⇒x=\frac{153}{9}\phantom{\rule{0ex}{0ex}}⇒x=17\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{are}17\mathrm{cm}\mathrm{and}23\mathrm{cm},\mathrm{that}\mathrm{is},\left(17+6\right)\mathrm{cm}.$

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