Question

one of the parallel sides of a trapezium is thrice the other . the area of the trapizium is 440 cm² and its height is 22 cm . find the length of its two parallel sides​

Answer 1

Given:

• One of the parallel sides of a trapezium is thrice the other.
• Area of trapezium is 440 cm².
• Height of trapezium is 22 cm.

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To find:

• Length of its two parallel sides?

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Solution:

One of the parallel sides of a trapezium is thrice the other.

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⠀⠀⠀⌬ Let the first side be x cm.

⠀⠀⠀⌬ Therefore, Second side is 3x cm.

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$\setlength{\unitlength}{1.5cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 22\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 3x\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf x\ cm }\end{picture}$

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We know that,

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$\star{\boxed{\sf{\purple{Area_{\;(trapezium)} = \dfrac{1}{2} \bigg(Sum\:of\;parallel\:sides \bigg) \times height}}}}$

Now, Putting values,

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$:\implies\sf 440 = \dfrac{1}{2} \bigg(x + 3x \bigg) \times 22$

$:\implies\sf 440 = \dfrac{1}{ \not{2}} \times \not{4}x \times 22$

$:\implies\sf 440 = 2x \times 22$

$:\implies\sf 440 = 44x$

$:\implies\sf x = \cancel{ \dfrac{440}{44}}$

$:\implies{\boxed{\sf{\pink{x = 10}}}}\;\bigstar$

Therefore,

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• First side, x = 10 cm

• Second side, 3x = 3 × 10 = 30 cm

Answer 2

Answer:

Given :

• Area of trapezium = 440 cm²
• Length of one parallel sides = 22 cm

To find :

Length of two other sides

Solution:

• Let the first side be x
• Second side = 3x

As we know that ,

$\huge \bf \: a \: = \frac{1}{2} \times sum \: \times height$

Putting values

$440 = \frac{1}{2} (3x + x) \times 22$

$440 = \frac{1}{2} (4x) \times 22$

$440 =</u><u> </u><u>2</u><u>x</u><u> </u><u>\</u><u>t</u><u>i</u><u>m</u><u>e</u><u>s</u><u> </u><u>2</u><u>2</u><u>$

$440 = 44x$

$x = \frac{440}{44}$

$x = 10$

First side = 10 cm

Second side = 3 × 10 = 30 cm