Question

The area of square field is 8184 m.square. A rectangular field, whose length is twice its breadth, has its perimeter equal to the perimeter of the square field. Find the area of rectangular field.

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find area of rectangular field.

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

• Area of square field = 8184m²

• perimeter of rectangle field = perimeter of square field.

• length of rectangular field is twice it's breadth.

$\star{\red {\bf\:Area \:of \:square = side \times\: side}}$

• Let side of square field be a

⇝Area of square field = 8184

⇝ a² = 8184

⇝ a = √8184

⇝ a = 90.4m

$\star{\red {\bf\:Perimeter\: of\: square = 4 \times\:side}}$

⇝perimeter of square field = 4 × a

⇝perimeter of square field = 4 × 90.4

⇝perimeter of square field = 361.6m

As it is given in the Question that perimeter of square field is equal to the perimeter of rectangular field .

So,

⇝ perimeter of rectangular field = 361.6m

And,

length of rectangular field is twice it's breadth.

Let breadth of rectangular field be x.

So, length of rectangular field = 2x

$\star{\red {\textbf{perimeter of rectangle = 2(l + b)}}}$

⇝ 2(2x + x) = 361.6

⇝ 3x = 361.6/2

⇝ x = 180.8/3

⇝ x = 60.2

So,

• Breadth = 60.2m
• length = 60.2×2 =120.4

As we know that,

$\star{\red {\bf\:Area \:of \:rectangle = l\times{b}}}$

Area of rectangular field = 60.2 × 120.4

Area of rectangular field = 7248 .08m²

Hence,

• Area of rectangular field is 7248.08m²

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Answer 2

$\purple {\bf {\underline {Given:-}}}$

• The area of square field is 8184 ${\sf {m^{2}}}$.
• A rectangular field's length is twice its breadth.
• It's perimeter equal to the perimeter of the square field.

$\purple {\bf {\underline {To\:Find:-}}}$

• The area of the rectangular field.

$\huge\purple {\bf {\underline {Solution:-}}}$

$\tt{The \: area \: of \: square \: field \: is \: 8184 \: {m}^{2} }$

$\tt{So, \: a \: side \: of \: the \: square \: field \: is = \sqrt{8184} \: m } \: = 90.47 \: m$

$∴ \tt{The \: perimeter \: of \: the \: square \: field \: =(4 \times 90.47) \: m = 361.88 \: m}$

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Let the breadth of the Rectangular Field be x

So, It's length is = 2x

We know that, in case of a Rectangular field,

$\red{ \bf{\star{ \: Perimeter = 2(length + breadth) }}}$

$∴ \tt{Perimeter \: of \: the \: rectngular \: field = 2(2x + x) \: m }$

$\tt{ = (2 \times 3x}) \:m$

$= \tt{6x \: m}$

According to the question,

$\tt{6x = 361.88}$

$⇒ \tt{x = \frac{361.88}{6} }$

$⇒ \tt{x = 60.31}$

✷ ${\bf { Breadth = 60. 31 \:m}}$

✷ ${\bf { Length = (2 × 60.31) \:m = 120.60\: m}}$

We know that, in case of rectangular field,

$\red{ \star {\bf{ \:Area = length \times breadth}}}$

∴ $\tt{Area \:of \:the \:Rectangular\: Field = (60.31 \times 120.60) \:m^{2}= 7273.386\:m^{2}}$

$\pink {\bf {Hence,\:the\:area\:of\:the\:rectngular \:field\:is\:7273.386\:m^{2}.}}$