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

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♠ Given :-

The numerical values of the area and perimeter

of a :

• Square Field = 7 : 4

• Square Park = 5 : 1

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♠ To Find :-

• Which of these has a greater side length?

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♠ Formulas Used :-

For any Square of Side a :

$\sf \large \left \{ {{Perimeter=4a} \atop {Area=a^2}} \right.$

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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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Answer 2

Given :-

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.

To Find :-

Which of these has a greater side length?

Solution :-

For field

Let the side of square field be a

Perimeter = 4 × side

Perimeter = 4 × a

Perimeter = 4a

Area = side × side

Area = a × a

Area = a²

Area/Perimeter = 7/4

a²/4a = 7/4

4 × (a²) = 7(4a)

4a² = 28a

4 × a × a = 28 × a

4a = 28

a = 28/4

a = 7

For park

Let the side of park be b

Perimeter = 4 × side

Perimeter = 4 × b

Perimeter = 4b

Area = side × side

Area = b × b

Area = b²

Area/Perimeter = 5/1

b²/4b = 5/1

1(b²) = 5(4b)

b² = 20b

b × b = 20 × b

b = 20

Hence

Square park has greater side