Question

The area of a squared pond is 1000 square m. A path of
uniform width is surrounded outside the pond and its area
is 369 square m. Find the outer length of the path.(Ans: 148​

Answer 1

$Given, \: Area \: of \: a \: squared \: pond \\ PQRS = 1000\:m^{2}$

$Area \: of \: path = 369 \:m^{2}$

$Let \: side \: of \: the \:square \: ABCD = s \:m$

$Area \: of \: the \: Outer \: square\: ABCD\\ = Area \: of \: PQRS + Area \: of \:the \:Path \\= 1000\:m^{2} + 369 \:m^{2} \\= 1369 \:m^{2}$

$\implies s^{2} = ( 37 \:m )^{2}$

$\implies s = 37 \:m$

$Now, Outer \: length \: of \: the \: path \\= Perimeter \: of \: Square \: ABCD \\= 4 \times s \\= 4 \times 37 \:m \\= 148 \:m$

Therefore.,

$\red { Outer \: length \: of \: the \: path} \green { = 148 \:m }$

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