Question

The area of a trapezium is 48cm2,the distance between parallel sides is 6cm.If one of the parallel sides is 4cm,find the other parallel side.

Answer 1

Please let me know if you need anything

Answer 2

$\begin{gathered}\frak{Given}\begin{cases}\sf{\:\;\:Area\:of\:the\:trapezium\:\bf{A=48\:cm^2}}\\\sf{\:\;\:Height\:of\:the\:trapezium\:\bf{h=6\:cm}}\\\sf{\:\;\:One\:of\:the\:parallel\:sides\:=\:\bf{4\:cm}}\end{cases}\end{gathered}$

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$\rm{\underline{\underline{To\:find:}}}\sf{The\:other\:parallel\:side.}$

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• $\sf{Let\:the\:other\:parallel\:side\:be\:x}$

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$\rm\underline{Now,using\:the\:formula\:of\:area\:of\:trapezium,}$

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$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{:\rightarrow\;Area\:of\:trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;sum\:of\:parallel\:sides\;\times\;height}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;48\;=\;\bf{\dfrac{1}{\cancel{2}}\;\times\;(4+x)\;\times\;\cancel{6}}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;48\;=\;\bf{\;(4+x)\;\times\;3}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;48\;=\;\bf{12+3x}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;48-12\;=\;\bf{3x}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;36\;=\;\bf{3x}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;3x\;=\;\bf{36}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;x\;=\;\bf{\cancel\dfrac{36}{3}}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;x\;=\;\bf{12}}}\end{gathered}$

$\begin{gathered}\:\underline{\boxed{\tt{Hence,the\:other\:parallel\:side\:=\:\bf{12\:cm}}}}\end{gathered}$