Question

The numerical values of the area and perimeter of a square field are in the ratio 7:4, while that of a square park are in the ratio 5:1. Which of these has a greater side length?

Answer 1

Answer:

perimeter of square are in ratio =5:2

sum of the ratio =5/7×180=128.57

length =5/7×180=51.42

square park in ratio =3:1

sum of the ratio =3x+1x=4x

lenght =3/4×180=135

breath =1/4×180=45

Answer 2

$-------------------------------</p><p></p><p>♠ Given :- </p><p></p><p>The numerical values of the area and perimeter</p><p>of a :</p><p></p><p>Square Field = 7 : 4</p><p></p><p>Square Park = 5 : 1 </p><p></p><p>-------------------------------</p><p></p><p>♠ To Find :- </p><p></p><p>Which of these has a greater side length?</p><p></p><p>-------------------------------</p><p></p><p>♠ Formulas Used :- </p><p></p><p>For any Square of Side a :</p><p></p><p>[tex] \sf \large \left \{ {{Perimeter=4a} \atop {Area=a^2}} \right.$

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♠ Solution :-

Let the Side length of Square Field be = x unit.

$\Large \bigstar \:   \underline{ \pmb{ \mathfrak{ \text{H}ence , }}}$

$\pmb {Area \: of \: Field = {x}^{2} } \\ \\ \pmb{ Perimeter \: of \: Field = 4x}$

$\large \bigstar \:\underline{ \pmb{ \mathfrak{ \text{A}ccording \:to \:the \:Given \:Condition}}}$

$\sf \dfrac{Area }{Perimeter} = \frac{7}{4} \\ \\ \dfrac{ {x}^{ \cancel2} }{ \cancel{4x}} = \frac{7}{ \cancel4} \\ \\ \LARGE\purple{ :\longmapsto\underline {\boxed{{\bf x = 7} }}}$

$\pmb{ \pink{ \underline{Hence \: Side \: length \: of \: the \: Field = 4\: unit}}}$

Let the Side length of Square Park be = y unit.

$\Large \bigstar \:   \underline{ \pmb{ \mathfrak{ \text{H}ence , }}}$

$\pmb {Area \: of \: Field = {y}^{2} } \\ \\ \pmb{ Perimeter \: of \: Field = 4y}$

$\large \bigstar \:\underline{ \pmb{ \mathfrak{ \text{A}ccording \:to \:the \:Given \:Condition}}}$

$\sf \dfrac{Area }{Perimeter} = \frac{5}{1} \\ \\ \dfrac{ {y}^{ \cancel2} }{ 4\: \cancel{y}} = \frac{5}{ 1} \\ \\ \LARGE\purple{ :\longmapsto\underline {\boxed{{\bf y = 20} }}}$

$\pmb{ \pink{ \underline{Hence \: Side \: length \: of \: the \: Field = 20\: unit}}}$

From Both We Clearly Get :

Side Length of Square Park is Greater than the Side Length of Square Field .

$\LARGE\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}$

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