Question

The area of a rectangle plot is 10 whole 3
/9 m2
. Find the length of the plot if its breadth is 2
whole1
/4m.​

Answer 1

${\purple{\underline{\underline{\mathtt{Answer\::}}}}}$

$\mathtt\orange{Breadth \: of\:rectangular\:plot\: = \: 4 \frac{16}{27 \: } \: m}$

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${\purple{\underline{\underline{\mathtt{Given\::}}}}}$

$\tt \: Area \: of \: rectangular \: plot \: = \: (10 \frac{3}{9} ) \: {m}^{2} \: = \: \frac{93}{9} \: {m}^{2} \\ \\ \tt \: Length \: of \: rectangular \: plot \: = \: 2 \frac{1}{4} \: m \: = \: \frac{9}{4} \: m$

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${\purple{\underline{\underline{\mathtt{To\:find\::}}}}}$

$\tt \: Breadth \: of \: rectangular \: plot \: = \: ?$

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${\underline{\pink{\mathfrak{Formula\:used\::}}}}$

$\mathtt{Area\:of\:rectangle\:=\:length\:×\:breadth}$

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${\underline{\pink{\mathfrak{According \:to\:question,}}}}$

$\tt \frac{93}{9} \: {m}^{2} = \: \frac{9}{4} \: m \: \times Breadth \\ \\ \tt \: \implies Breadth \: = \: ( \frac{93}{9} \: \div \: \frac{9}{4} ) \: m \\ \\ \tt \: \implies Breadth \: = \: ( \frac{ \cancel93}{ \cancel9} \: \times \: \frac{ 4}{9} ) \: m \\ \\ \tt \: \implies Breadth = \: \frac{ 31 \times 4}{ 3 \times 9} \: m \:$

$\mathtt\green{\implies \: Breadth \: = \: \frac{124}{27} \: m \: = \: 4 \frac{16}{27 \: } \: m}$

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${\purple{\underline{\underline{\mathtt{Answer\:Verification}}}}}$

$\tt \: Area \: = Length \: \times Breadth$

$\bf{Substituting,}$

$\tt \: \: \implies\frac{93}{9} \: {m}^{2} = \: \frac{9}{4} \: m \: \times \: \frac{124}{27} \: m \\ \\ \tt \: \implies \cancel\frac{93}{9} \: {m}^{2} \: = \: ( \ \cancel\frac{9}{4} \: \times \: \cancel \frac{124}{27} ) \: {m}^{2}$

$\mathtt\orange{\implies\frac{31}{3} \: {m}^{2} \: = \: \frac{31}{3} \: {m}^{2} }$

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${\green{\underline{\bf{Hence,\:Verified.}}}}$