Question

SECTION-B
Simplify @)* ) and express the result in exponential fom
The area of a trapezium is 180 em and its height is 9 cm. If one of the parallelade is longer th
the other by 6cm, find the two parallel sides
Sove
1
SECTION - C​

Answer 1

Appropriate Question:

• The area of a trapezium is 180 cm². And it's height is 9 cm. If one of the parallel sides is longer than the other by 6 cm. Find the two || sides.

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❍ Let's say, that one of the || side of trapezium be x cm.

Given that,

• If one of the // side of the trapezium is longer than the other by 6 cm.

Therefore,

• Other // side = (x + 6) cm.

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$\underline{\bf{\dag} \:\mathfrak{Area\;of\: trapezium\: :}}$⠀⠀⠀⠀

To find area formula of the trapezium is given by :

$\bf{\dag}\:\boxed{\sf{Area_{\;(trapezium)} = \dfrac{1}{2} \times \Big(a + b\Big)\times h}}$

where,

• a & b are the parallel sides of the trapezium. And, h is the height of the trapezium.
• Area of trapezium is given that is 180 cm².

$:\implies\sf 180 = \dfrac{1}{2} \times \Big(x + x + 6\Big) \times 9 \\\\\\:\implies\sf 180 = \dfrac{1}{2} \times \Big(2x + 6\Big) \times 9 \\\\\\:\implies\sf 2x + 6 = \bigg(\dfrac{\cancel{180}^{\:\;20} \times 2}{\cancel{\;9}}\bigg)\\\\\\:\implies\sf 2x + 6 = 20 \times 2 \\\\\\:\implies\sf 2x + 6 = 40 \\\\\\:\implies\sf 2x = 40 - 6 \\\\\\:\implies\sf 2x = 34 \\\\\\:\implies\sf x = \cancel\dfrac{34}{2} \\\\\\:\implies\underline{\boxed{\pmb{\frak{\purple{x = 17}}}}}\;\bigstar$

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★ Finding, the another // side :

➟ Other // side = ( x + 6 )

➟ Other // side = 17 + 6

➟ Other // side = 23 cm

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$\therefore{\underline{\textsf{Hence, \;the\;two\;parallel\; sides\:are\;\textbf{9 cm}\;\sf{and}\:\textbf{23 cm}.}}}$

Answer 2

Given :-

Area of trapezium = 180 cm

Height = 9 cm

Other parallel side is longer by 6 cm

To Find :-

Length of  the two parallel sides

Solution :-

Let

Parallel side (1) = x

Parallel side (2) = x + 6

$\dashrightarrow \bf Area_{(Trapezium)} = \dfrac{1}{2} \times (a+b)\times h$

Now

$\sf 180 = \dfrac{1}{2} \times (x+x+6) \times 9$

$\sf 180 \times 2 = (2x+ 6) \times 9$

$\sf 360 = 2x + 6 \times 9$

$\sf \dfrac{360}{9} = 2x + 6$

$\sf 40 = 2x+6$

$\sf 40-6=2x$

$\sf 34 = 2x$

$\sf\dfrac{34}{2} = x$

$\sf 17 = x$

Parallel sides are

x = 17 cm

x + 6 = 17 + 6 = 23 cm