Question

the area of trapezium is 180 cm^2 and its height is 15cm. if one of the parallel side is double of other, find the length of two parallel sides

Answer 1

Given :

• Area of Trapezium is 180 cm² .
• Height of Trapezium is 15 cm .
• One parallel side of trapezium is double of other .

To Find :

• Length of two Parallel Sides .

Solution :

$\longmapsto\tt{Let\:one\:Parallel\:Side\:be=x}$

As Given that One parallel side of trapezium is double of other . So ,

$\longmapsto\tt{Other\:Parallel\:Side=2x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{180=\dfrac{1}{2}\times{(x+2x)}\times{15}}$

$\longmapsto\tt{180\times{2}=(x+2x)\times{15}}$

$\longmapsto\tt{360=15x+30x}$

$\longmapsto\tt{360=45x}$

$\longmapsto\tt{x=\cancel\dfrac{360}{45}}$

$\longmapsto\tt\bf{x=8}$

Value of x is 5 .

Therefore :

$\longmapsto\tt{One\:parallel\:side=x}$

$\longmapsto\tt\bf{8\:cm}$

$\longmapsto\tt{Other\:parallel\:side=2(8)}$

$\longmapsto\tt\bf{16\:cm}$

So , The Length of Two parallel sides are 8 cm and 16 cm .

Answer 2

Given

• Area of a trapezium is 180cm².
• Height = 15cm
• One parallel side is double of the other parallel side.⠀

⠀

To find

• Length of two parallel sides.⠀

⠀

Solution

• Let the one parallel side be x, then the other parallel side be 2x.⠀

⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀Required Diagram

⠀

• Using Formula

$\large{\boxed{\boxed{\sf{Area_{(Trapezium)} = \dfrac{Sum\: of\: parallel\: lines}{2} \times height}}}}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 180}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{x + 2x}{2} \times 15 = 180}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{3x}{2} = \dfrac{180}{15}}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{3x}{2} = 12}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {3x = 24}$⠀

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{24}{3}}$⠀

⠀

$\bf:\implies\: \: \: \: \: \: \: \: {x = 8}$⠀

⠀

• We have, x = 8⠀⠀⠀⠀⠀

⠀

By putting the value of x⠀

❍ First parallel side = x = 8cm

❍ Second parallel side = 2x = 16cm

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