Question

The area of a rectangular field is 286 3/4 sq m. If the length of the field is 18 1/2m, find the breadth of the field.

Answer 1

$\bf \: \underline{ Given} :$ ↴

$\sf \: The \: area \: of \: a \: rectangular \: field \: is \: 286 \: \dfrac{3}{4} \:m ^{2}$

$\sf \: The \: length \: of \: the \: field = 18 \: \dfrac{1}{2} \: m$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: breadth \: of \: that \: field.$

$\sf \: As \: we \: know \: that :$ ↴

$\sf \boxed{ \pink{ \sf \: \:Area\:of\:Rectangle=l\times{b}}}$

$\sf \: Where,$

$\bull \longrightarrow \: \sf \: L = Length$

$\bull \longrightarrow \: \sf \: B = Breadth$

$\sf \: Let \: the \: Breadth \: of \: the \: rectangular \: field \: be \: x.$

$\sf \: Putting \: the \: values,$

$\sf \:\implies \:286 \: \dfrac{3}{4}=18 \: \dfrac{1}{2}\times{x}$

$\sf \: Convert \: 286 \: \dfrac{3}{4} \: and \: 18 \: \dfrac{1}{2}\: \: into \:improper \: fraction.$

$\sf \:\implies \dfrac{1147}{4} =\dfrac{37}{2}\times{x}$

$\sf \: \implies \: 286.75 = 18.5\times{x}$

$\sf \: \implies \: x = \dfrac{286.75 }{18.5}$

$\sf \: \implies \: x = 15.5 \: or \: 15 \: \dfrac{1}{2}$

$\underline{ \boxed{ \pink{ \sf \: So, \: The \: breadth \: of \: the \: rectangular \: field \: is \: 15 \: \dfrac{1}{2} \: m}}}$

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$\bf \underline{\:Related \: formulas} :$ ↴

$\sf \: 1. \: Area of Rectangle = l × b$

$\sf \: 2. \: Perimeter \: of \: Rectangle = 2 \: (l + b)$

$\sf \: 3. \: Area \: of \: Square = Side × Side$

$\sf \: 4. \: Perimeter \: of \: Square = 4 × Side$

$\sf 5. \: Diagonal \: of \: Rectangle = \sqrt{l ^{2} + b^{2}}$