Question

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A rectangular plot of land is 25 3/4m long and 15 2/3m wide. Find the perimeter and area of the plot.​

Answer 1

Given

$\tt \implies Length(l) = 25 \dfrac{3}{4} = \dfrac{103}{4} m \\ \\ \tt \implies Breadth(b) = 15 \dfrac{2}{3} = \dfrac{47}{3} m$

Formula

$\tt \implies Perimeter \: of \: rectangle= 2(l + b) \\\tt \implies Area \: of \: rectangle= l \times b$

Answer

✏ Perimeter of rectangular plot:

$\tt \implies = 2(length + breadth) \\ \\ \tt \implies = 2( \dfrac{103}{4} + \dfrac{47}{3} ) \\ \\ \tt \implies = 2 \times ( \dfrac{3 \times 103 + 4 \times 47}{4 \times 3} ) \\ \\ \tt \implies = 2 \times ( \dfrac{309 + 188}{12} ) \\ \\ \tt \implies = 2 \times ( \dfrac{497}{12} ) \\ \\ \tt \implies = \frac{497}{6} \\ \\ \large \implies \boxed {\boxed {\tt \blue {= 82.8m {}^{2} }}}$

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✏ Area of rectangular plot:

$\tt \implies = length \: \times \: breadth \\ \\ \tt \implies = \dfrac{103}{4} \times \dfrac{47}{3} \\ \\ \tt \implies = \frac{4841}{12} \\ \\ \large \implies \boxed {\boxed {\tt \blue { = 403.41m {}^{2} }}} </p><p>$

Answer 2

Given ,

$\star \: \sf Length = 25 \frac{3}{4} \: \: m \\ \\ \star \: \sf</p><p>Breadth = 15 \frac{2}{3} \: \: m$

We know that , the perimeter of rectangle is given by

$\sf \large \star \: \: \fbox{Perimeter = 2(l + b) }$

Thus ,

$\sf \mapsto Perimeter = 2( 25 \frac{3}{4} + 15 \frac{2}{3} ) \\ \\ \sf \mapsto Perimeter = 2( \frac{103}{4} + \frac{47}{3} ) \\ \\ \sf \mapsto Perimeter = 2( \frac{309 + 188}{12} ) \\ \\ \sf \mapsto Perimeter = \frac{497}{6} \\ \\ \sf \mapsto Perimeter =82.2 \: \:m$

$\therefore \sf \underline{The \: perimeter \: of \: rectangle \: is \: 82.2 \: m}$

We know that , the area of rectangle is given by

$\star \: \: \large \sf \fbox{Area = length \times breadth }$

Thus ,

$\sf \mapsto Area = 25 \frac{3}{4} \times 15 \frac{2}{3} \\ \\ \sf \mapsto Area = \frac{103}{4} + \frac{47}{3} \\ \\ \sf \mapsto Area = \frac{4841}{12} \\ \\ \sf \mapsto Area = 403.41 \: \: {m}^{2}$

$\therefore \sf \underline{The \: area \: of \: rectangle \: is \: 403.41 \: {m}^{2} }$