Question

The parallel sides of a traperium are in the ratio 2:3, its height is 20cm and area is 500 cm ² find the length of the parallel sides

please ans me​

Answer 1

Answer:

Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf{20\ cm} }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf{30\ cm} }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf{20\ cm} }\end{picture}$

$\begin{gathered}\end{gathered}$

Given :

• ➠ The parallel sides of a traperium are in the ratio 2:3.
• ➠ The height of trapezium is 20cm.
• ➠ Area of trapezium is 500 cm².

$\begin{gathered}\end{gathered}$

To Find :

• ➠ The length of the parallel sides.

$\begin{gathered}\end{gathered}$

Using Formula :

${\longrightarrow{\small{\underline{\boxed{ \sf{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}}}}}}$

$\begin{gathered}\end{gathered}$

Solution :

Let :-

• The parallel sides be trapezium be 2x and 3x.

Now, according to the question :-

${\dashrightarrow{\small{\sf{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = \dfrac{1}{2}\times{(2x + 3x)}\times{20}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = \dfrac{1}{2}\times{(5x)}\times{20}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = \dfrac{1 \times 5x \times 20}{2}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = \dfrac{100x}{2}}}}}$

${\dashrightarrow{\small{\sf{x = \dfrac{500 \times 2}{100}}}}}$

${\dashrightarrow{\small{\sf{x = \dfrac{1000}{100}}}}}$

${\dashrightarrow{\small{\sf{x = \cancel{\dfrac{1000}{100}}}}}}$

${\dashrightarrow{\small{\sf{x = 10 \: cm}}}}$

Therefore :-

• Lenght of first parallel side = 2x = 2×10 = 20 cm
• Lenght of second parallel side = 3x = 3×10 = 30 cm

∴ The length of parallel sides of trapezium is 20 cm and 30 cm.

$\begin{gathered}\end{gathered}$

Verification :

${\dashrightarrow{\small{\sf{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} =\dfrac{1}{2}\times{(20 + 30)}\times{20}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} =\dfrac{1}{2}\times{(50)}\times{20}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} =\dfrac{1}{2}\times{50}\times{20}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} =\dfrac{1 \times 50 \times 20}{2}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} =\dfrac{1000}{2}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = \cancel{\dfrac{1000}{2}}}}}}$

${\dashrightarrow{\small{\sf{500 \: {cm}^{2} = 500 \: {cm}^{2} }}}}$

${\dashrightarrow{\small{\sf{ LHS = RHS}}}}$

∴ Hence Verified!

$\begin{gathered}\end{gathered}$

Learn More :

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}\end{gathered}\end{gathered}\end{gathered}$

$\underline{\rule{200pt}{2.5pt}}$

Answer 2

Answer:

So the sides are given in the ratio = 2:3

Let it be 2xand3x

Area of trapezium= 1/2[sum of parallel sidesxheight]

1/2[(2x+3x)x20] = 500 cm^2

1/2[5xx20]= 500cm^2

5x=(500x2)=20 x=(500x2)÷(20×5)

x=1000÷100

x=10

2x=2(10)=20.

3x=3(10)=30.

Hence sides are 20cm and 30cm

Step-by-step explanation:

Please mark it Brainliest answer