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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HERE IS UR ANSWER

1) Given:-

The numerical values of the area and perimeter

of a :-

• Square Field = 7: 4
• Square Park = 5: 1

2) To find :-

• Which of these has a greater side length ?

3) Formulas used :-

• Perimeter = 4a
• Area = a²

4) Solution :-

• Let the side of square Field be = x unit

5) Hence,

• Area of field = x²
• Perimeter of field = 4x

6) According to the given condition :-

• Area/ Perimeter = 7/4
• x²/4x =7/4

(Here ² , 4x and 4 will get cancelled )

• x = 7

Hence side length of the field =4 unit

• Let the side length of Square Park be = y unit

7) Hence,

• Area of field = y²
• Perimeter of field = 4y

8) According to the given condition :-

• Area/Perimeter = 5/1
• y²/4y = 5/1

( Here ² and y gets cancelled )

• y=20

Hence side length of field=20unit

FROM BOTH WE CLEARLY GET :-

Side length of Square Park is greater than the side length of Square field .

HOPE IT HELPS U ✌✌✌✌

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

$\longrightarrow$Perimeter = 4 × side

$\longrightarrow$Perimeter = 4 × a

$\longrightarrow$Perimeter = 4a

Area = side × side

Area = a × a

Area = a²

$\implies$Area/Perimeter = 7/4

$\longrightarrow$a²/4a = 7/4

$\longrightarrow$4 × (a²) = 7(4a)

$\longrightarrow$4a² = 28a

$\longrightarrow$4 × a × a = 28 × a

$\longrightarrow$4a = 28

$\longrightarrow$a = 28/4

$\longrightarrow$a = 7

For park

Let the side of park be b

$\longrightarrow$Perimeter = 4 × side

$\longrightarrow$Perimeter = 4 × b

$\longrightarrow$Perimeter = 4b

$\implies$Area = side × side

$\longrightarrow$Area = b × b

$\longrightarrow$Area = b²

Area/Perimeter = 5/1

$\longrightarrow$b²/4b = 5/1

$\longrightarrow$1(b²) = 5(4b)

$\longrightarrow$b² = 20b

$\longrightarrow$b × b = 20 × b

$\longrightarrow$b = 20

Hence,

Square park has greater side