Question

the area of a trapezium is 0.05m² and its height is 20 CM. If one of the parallel side is shorter than the other by 8 CM, find the length of the longer side ​

Answer 1

Answer:

$\begin{gathered}\sf Given \begin{cases} & \sf{Area\:of\: trapezium = 0.05\:m^2 = \bf{500\:cm^2}} \\ & \sf{Height\:of\: trapezium = \bf{20\:cm}} \end{cases}\\ \\\end{gathered}$

To find: Length of longer side?

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$\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}$

One of the parallel side of trapezium is shorter than the other by 8 cm.

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Now,

☯ Let one side of trapezium be x cm.

Therefore, Other side will be (x + 8) cm.

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$\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}$

⋆ Area of trapezium is given by,

$\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}\\ \\\end{gathered}$

Where,

a and b are two parallel sides of trapezium and h is the Distance between them or height of trapezium.

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$\begin{gathered}\dag\;{\underline{\frak{Now,\:Putting\:given\:values\:in\;formula,}}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 500 = \dfrac{1}{2} \times (x + (x + 8)) \times 20\\ \\ \\ :\implies\sf 500 = \dfrac{1}{2} \times (2x + 8) \times 20\\ \\ \\ :\implies\sf 500 \times 2 = (2x + 8) \times 20\\ \\ \\ :\implies\sf 1000 = (2x + 8) \times 20\\ \\ \\ :\implies\sf \cancel{ \dfrac{1000}{20}} = (2x + 8)\\ \\ \\ :\implies\sf 50 = (2x + 8)\\ \\ \\ :\implies\sf 50 - 8 = 2x\\ \\ \\ :\implies\sf 42 = 2x\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{42}{2}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 21}}}}}\;\bigstar\\ \\\end{gathered}:$

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Therefore,

One parallel side of trapezium, x = 21 cm

Other parallel side of trapezium, (x + 8) = 29 cm

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$\therefore\:{\underline{\sf{Hence,\:the\:two\:parallel\:sides\:of\: trapezium\:are\: \bf{21\:cm\:and\:29\:cm}.}}}$

Answer 2

$\begin{gathered}\begin{gathered}\sf Given \begin{cases} & \sf{Area\:of\: trapezium = 0.05\:m^2 = \bf{500\:cm^2}} \\ & \sf{Height\:of\: trapezium = \bf{20\:cm}} \end{cases}\\ \\\end{gathered}\end{gathered}$

To find: Length of longer side?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\begin{gathered}\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}\end{gathered}$

One of the parallel side of trapezium is shorter than the other by 8 cm.

⠀⠀⠀⠀

Now,

☯ Let one side of trapezium be x cm.

Therefore, Other side will be (x + 8) cm.

⠀⠀⠀⠀

$\begin{gathered}\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}\end{gathered}$

⋆ Area of trapezium is given by,

$\begin{gathered}\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}\\ \\\end{gathered}\end{gathered}[tex]</p><p></p><p>Where,a and b are two parallel sides of trapezium and h is the Distance between them or height of trapezium.</p><p>⠀⠀⠀⠀</p><p>[tex]\begin{gathered}\begin{gathered}\dag\;{\underline{\frak{Now,\:Putting\:given\:values\:in\;formula,}}}\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}:\implies\sf 500 = \dfrac{1}{2} \times (x + (x + 8)) \times 20\\ \\ \\ :\implies\sf 500 = \dfrac{1}{2} \times (2x + 8) \times 20\\ \\ \\ :\implies\sf 500 \times 2 = (2x + 8) \times 20\\ \\ \\ :\implies\sf 1000 = (2x + 8) \times 20\\ \\ \\ :\implies\sf \cancel{ \dfrac{1000}{20}} = (2x + 8)\\ \\ \\ :\implies\sf 50 = (2x + 8)\\ \\ \\ :\implies\sf 50 - 8 = 2x\\ \\ \\ :\implies\sf 42 = 2x\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{42}{2}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 21}}}}}\;\bigstar\\ \\\end{gathered}:\end{gathered}</p><p>\begin{gathered}\begin{gathered}\dag\;{\underline{\frak{Now,\:Putting\:given\:values\:in\;formula,}}}\\ \\\end{gathered}\end{gathered}$

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Therefore,

One parallel side of trapezium, x = 21 cm

Other parallel side of trapezium, (x + 8) = 29 cm

$\therefore\:{\underline{\sf{Hence,\:the\:two\:parallel\:sides\:of\: trapezium\:are\: \bf{21\:cm\:and\:29\:cm}.}}}$