Question

the ratio of the parralel side of a trapezium is 2 : 3 . The distance between them is 15 CM. If the area of the trapezium is 600 m² , find the length of the parallel side. ​

Answer 1

Answer:

given ratio of parallel sides is 2:3

let the first side be 2x and the second side be 3x

height of the distance between parallel sides is given 15 CM

so using the formula of area of trapezium

area of trapezium = 1/2(sun of parallel sides) × h

600 = 1/2(2x+3x) × 15

1200= 5x ×15

1200/15= 5x

80= 5x

x= 80/5

x=16

therefore 2x = 2×16 = 32cm

similarly 3x = 3× 16 = 48cm

show the length of parallel sides is 32 cm and 48 cm

hope it's helpful

Answer 2

Appropriate Question:

• The ratio of the parralel side of a trapezium is 2 : 3. The distance between them is 15 cm. If the area of the trapezium is 600 cm² , find the length of the parallel side.

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$\sf Given \begin{cases} & \sf{Ratio\:of\: parallel\: sides = \bf{2:3}} \\ & \sf{The\: distance\:between\: parallel\:sides = \bf{15\:cm}} \\ & \sf{Area\:of\: trapezium = \bf{600\:cm^2}} \end{cases}$

To find: Length of parallel sides?

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☯ Let the parallel sides of a trapezium be 2x and 3x cm.

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⋆ DIAGRAM:

$\setlength{\unitlength}{1.3cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 15\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 3x\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 2x\ cm }\end{picture}$

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

⋆ Area of trapezium is given by,

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

Where,

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

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$\dag\;{\underline{\frak{Now,\:Putting\:values\:in\:formula,}}}$

$:\implies\sf 600 = \dfrac{1}{2} \times (2x + 3x) \times 15\\ \\ \\ :\implies\sf 600 = \dfrac{1}{2} \times 5x \times 15\\ \\ \\ :\implies\sf 600 \times 2 = 5x \times 15\\ \\ \\ :\implies\sf 1200 = 75x\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{1200}{75}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 16}}}}}\;\bigstar$

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Therefore, Parallel sides of trapezium are,

• 2x = 2 × 16 = 32 cm

• 3x = 3 × 16 = 48 cm

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$\therefore\:{\underline{\sf{Hence,\:The\: length\:of\: parallel\:sides\:are\:32\:cm\:and\:48\:cm.}}}$