Question

area of trapezium =405m^2 parrel sides ratio =4:5.. distance between =18 find length of parrallel sides
GIVE STEP BY STEP EXPLAINATION ​

Answer 1

Answer:

Length of parllel sides are 20. and 25m

Explanation:

Area of a trapezium :-

→ ½(a + b)h

Where,

• a and b denotes the parallel sides.
• h is the distance between parallel sides.

We are given with,

• Area = 405m²
• Ratio of a : b = 4 : 5
• h = 18m

Let's say the parallel sides are 4x and 5x

According to the question,

→ 405 = ½(4x + 5x)18

→ 405 = ½(9x)18

→ 405 = (9x)9

→ 405 = 81x

→ 405/81 = x

→ 5 = x

∴ x = 5

So, the parallel sides are :-

• 4x = 4(5) = 20m
• 5x = 5(5) = 25m

Hence, the parallel sides are 20m & 25m.

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Formula used :

Area of a trapezium :-

→ ½(sum of parallel side)(distance between them)

Answer 2

$\Huge \orange \dag \: \Huge \underbrace{\textrm{{{\color{blue}{Given}}}}} \: \orange \dag$

Area of trapezium = 405 m².

Ratio of parallel sides are 4 : 5.

Distance between parallel sides = 18 m.

Or,

Height = 18 m.

_________________________

$\Huge \orange \dag \: \Huge \underbrace{\textrm{{{\color{blue}{To \: \: Find}}}}} \: \orange \dag$

Length of parallel sides.

________________________

$\Huge \orange \dag \: \Huge \underbrace{\textrm{{{\color{blue}{Formula \: \: Using}}}}} \: \orange \dag$

$\large\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: trapezium \: = \: \frac{1}{2} \: \times \: h \: \times \: (a + b) }}}}}\end{gathered}$

• H denotes height of trapezium.

• a and b denotes parallel sides of trapezium.

_______________________

$\Huge \orange \dag \: \Huge \underbrace{\textrm{{{\color{blue}{Solution}}}}} \: \orange \dag$

Let , the parallel sides of trapezium be 4x and 5x respectively.

According to the question

$\large\begin{gathered} {\underline{\boxed{ \rm {{405 \: = \: \frac{1}{2} \: \times \: 18 \: \times \: ( \: 4x \: + \: 5x \: ) \: }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{405 \: = \: \cancel\frac{1} {2} \: \times \: \cancel{18} \: \: ^{9} \: \times \: ( \: 9x ) \: }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{405 \: = \: 9 \: \times \: 9x \: }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{405 \: = \: 81x }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{ \frac{405}{81} \: = \:x }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{ \cancel\frac{405} {81} \: ^{5} \: = \:x }}}}}\end{gathered}$

$\large\begin{gathered} {\underline{\boxed{ \rm {{ 5 \: = \: x }}}}}\end{gathered}$

$\Large\begin{gathered} {\underline{\boxed{ \rm {\red{x \: = \: 5}}}}}\end{gathered}$

So , the parallel sides of trapezium is :-

$\bf \large \rightarrow \: 4x \: = \: 4 \: \times \: 5 \: = \: 20 \: m$

$\bf \large \rightarrow \: 5x \: = \: 5 \: \times \: 5 \: = \: 25 \: m$

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Hence , the parallel sides of trapezium is 20 m and 25 m.