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

$\frak{Given} \begin{cases} \sf Area\:of\:trapezium\: = \frak{540\:cm^2} & \\ \\ \sf Height\:of\:trapezium\: = \frak{18\:cm}& \end{cases}$

❍ Let's consider one of the parallel side of trapezium be x cm.

Then, other parallel side will be (x + 12) cm.

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The Area of trapezium is given by,

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

Where,

• a and b are two parallel sides of trapezium.
• And, h is the height or distance between two parallel sides of trapezium.

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

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

Answer 2

Answer:

Given :-

• Area of trapezium = 540 cm²
• Altitude = 18 cm
• One parallel side = 12 + Other parallel side

To Find :-

Both parallel sides

Solution :-

Let the parallel sides be x and x + 12

$\sf \: area = \dfrac{1}{2} \times (a + b) \times h$

$\sf \: 540 = \dfrac{1}{2} \times (x + x + 12) \times 18$

$\sf \: 540 = 9(2x + 12)$

$\sf \: \dfrac{540}{9} = 2x + 12$

$\sf \: 60 = 2x + 12$

$\sf \: 2x = 60 - 12$

$\sf \: 2x = 48$

$\sf \: x \: = \dfrac{48}{2}$

$\sf \: x \: = 24$

Parallel sides

x = 24

x + 12 = 24 + 12 = 36 cm