Question

Mr. Apoloan wants to lay out a rectangular playground which will contain 30 square feet . The desired length will be 7 times the width. ​

Answer 1

$Let \: the \:width \:of \: rectangular \:play \\ground (w) = x \:m$

$Length (l) = 7 \: times \: the \:width\\= 7x \: m$

$\blue { Area \: of \: the \:play \: ground}\\\blue{= 30 \: square \: feet } \: (given)$

$\implies l \times w = 30$

$\implies 7x \times x = 30$

$\implies x^{2} = \frac{30}{7}$

$\implies x = \sqrt{ \frac{30}{7}}\: feet$

$Length (l) = 7 x \\= 7 \times \sqrt{ \frac{30}{7}}\: feet$

$= \sqrt{7} \times \sqrt{30} \\= \sqrt{210} \: feet$

Therefore.,

$\underline{\pink{Dimensions \:of \:the \:play \: ground :}}$

$Length = \sqrt{210} \: feet$

$Width = \sqrt{ \frac{30}{7}}\: feet$

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