Question

Find the length of the side of a square playground, whose area is equal to
the area of a rectangular field of dimensions 72m x 338m.​

Answer 1

Given : Area of a square playground is equal to the rectangular playground whose dimensions are 72m × 338m .

To Find : Length of the side of the square playground.

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Here

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• Length of the rectangle = 338m
• Breadth of the rectangle = 72m

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As we know that :

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$\underline{\boxed{\sf\purple{\bigstar \: area \: of \: the \: rectangle \: = l \times b}}}$

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Where

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• l denotes length of the rectangle.
• b denotes breadth of the rectangle.

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Put the values in the formula and solve -

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$\sf\implies \: area \: of \: the \: rectangular \: park \: = l \times b \\ \\ \\ \sf\implies \: area \: of \: the \: rectangular \: park \: = 338 \times 72 \\ \\ \\ \sf\implies \: area \: of \: the \: rectangular \: park \: = \underline{\boxed{\sf\purple{24336 {m}^{2} }}} \bigstar$

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Here, it is given that

Area of the rectangular playground = Area of the square playground

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As we know that :

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$</p><p> \underline{\boxed{\sf\purple{\bigstar \: area \: of \: a \: square \: = {side}^{2} }}}$

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Now, put the value of area and solve -

$\: \:$

$\sf:\implies \: area \: of \: the \: square \: park \: = {side}^{2} \\ \\ \\ \sf:\implies \: 24336 = {side}^{2} \\ \\ \\ \sf:\implies \: side \: = \sqrt{24336} \\ \\ \\ \sf:\implies \: side \: = \underline{\boxed{\sf\purple{156 {m}^{2} }}}\bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: side \: of \: the \: circular \: park \: is \: \bold{156 {m}}^{2} }}$