Question

The area of trapezium is 540 cm2 and the altitude is 18cm. If one of

the parallel sides is 12cm longer than the other. Find the length of

both the parallel sides.​

Answer 1

Given Data :

• Area of trapezium = 540 cm²
• Height of trapezium = 18 cm

　　　　　　　　 

To Find :

• Both parallel sides

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✞ Let one parallel side of trapezium be $x$ and other parallel side will be ${x \: + \: 12}$

　　　　　　　　　　　 

The Area of trapezium :

$\star\:{\underline{\boxed{\frak{\blue{Area_{\:(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}}$

　　　　　　　　　　　 

Here,

• a and b are parallel side of trapizium. Where as h is height or distance between 2 parallel lines.

　　　　　　　　 

${\underline{\rm\blue{❖\:Substituting\:given\:values\:in\:formula,}}}\\\\\\\ :\implies\sf 540= \dfrac{1}{\cancel{2}} \times \bigg((x) + (x + 12) \bigg) \times \cancel{18}\\\\\\ :\implies\sf 540 = (2x + 12) \times 9\\\\\\ :\implies\sf (2x + 12) = \cancel{\dfrac{540}{9}}\\\\\\ :\implies\sf (2x + 12) = 60\\\\\\ :\implies\sf 2x = 60 - 12\\\\\\ :\implies\sf 2x = 48\\\\\\ :\implies\sf x =\cancel{\dfrac{48}{2}}\\\\\\ :\implies{\boxed{\frak{\blue{x = 24}}}}\:\bigstar$

⠀⠀⠀⠀

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Hence, Length of both parallel sides is 24 cm and 36 cm respectively.

Answer 2

Step-by-step explanation:

$\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}$

${\bold{\sf{Area \: of \: trapezium \: = \: 540cm²}}}$

${\bold{\sf{Altitude \: = \: 18cm}}}$

${\bold{\sf{Let \: one \: parallel \: side \: be \: x \: and \: other \: be \: (x + 12)}}}$

${\bold{\sf{We \: know \: that \: area \: of \: trapezium \: is,}}}$

${\bold{\sf{\red{\frac{1}{2} \: × \: (sum \: of \: parallel \: sides) \: × \: h}}}}$

${\bold{\sf{\underline{According \: to \: the \: question,}}}}$

${\bold{\sf{→ \: \frac{1}{2} \: × \: (x + x + 12) \: × \: 18 \: = \: 540}}}$

${\bold{\sf{→ \: 2x \: + \: 12 \: × \: 9 \: = \: 540}}}$

${\bold{\sf{→ \: 2x \: + \: 12 \: = \: \frac{540}{9}}}}$

${\bold{\sf{→ \: 2x \: + \: 12 \: = \: 60}}}$

${\bold{\sf{→ \: 2x \: = \: 60 \: - \: 12}}}$

${\bold{\sf{→ \: 2x \: = \: 48}}}$

${\bold{\sf{→ \: x \: = \: \frac{48}{2}}}}$

${\bold{\sf{ \: → \: x \: = \: 24 cm}}}$

${\bold{\sf{→ \: (x +12) \: = \: 24 \: + \: 12 cm}}}$

${\bold{\sf{→ \: 36cm}}}$

${\bold{\sf{\fbox{\purple{One side = 24cm}}}}}$

${\bold{\sf{\fbox{\purple{Other side = 36cm}}}}}$