Question

The sides of a rectanglular plot are in the ratio 5:4. It's area is equal to 500 sqm.find the perimeter of the plot .​

Answer 1

Given :

• The sides of a rectanglular plot are in the ratio 5:4. It's area is equal to 500 sqm.

To Find :

• The perimeter of rectangular plot = ?

Solution :

Let Length of rectangular plot be 5x and Breadth of rectangular plot be 4x.

• Area of rectangular plot = 500 m²

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★ Finding the dimensions of rectangle :

→ Area of rectangle = Length * Breadth

→ 500 = 5x * 4x

→ 500 = 20x²

→ 500 ÷ 20 = x²

→ x² = 500 ÷ 20

→ x² = 50 ÷ 2

→ x² = 25

→ x = √25

→ x = 5 m

★ D I M E N S I O N S :

➝ Length of rectangle = 5x

➝ Length of rectangle = 5(5)

➝ Length of rectangle = 25 m

➸ Breadth of rectangle = 4x

➸ Breadth of rectangle = 4(5)

➸ Breadth of rectangle = 20 m

• Hence, Length of rectangular plot is 25 m and Breadth of rectangular plot is 20 m.

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★ Let's find the perimeter of rectangle :

⋙ Perimeter of rectangle = 2(Length + Breadth)

⋙ Perimeter of rectangle = 2(25 + 20)

⋙ Perimeter of rectangle = 2(45)

⋙ Perimeter of rectangle = 90 m

• Hence,the perimeter of rectangular plot is 90 m.

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Answer 2

Given:-

• Ratio of the sides of rectangular plot = 5:4
• Area of Rectangular plot = 500m²

Find:-

• Perimeter of the plot.

Solution:-

Let, Length of Rectangular plot = ❝5x❞ m

and, Breadth of Rectangular plot = ❝4x❞ m

Now, we know that

⟼ Area of Rectangle = Length × Breadth

where,

• Length, l = ❝5x❞ m
• Breadth, b = ❝4x❞ m
• Area of Rectangle = 500m²

❍ Substituting these values ❍

➺ Area of Rectangle = l × b

➺ 500 = 5x × 4x

➺ 500 = 20x²

➺ 500/20 = x²

➺ 50/2 = x²

➺ 25 = x²

➺ x = √(25)

➺ x = 5m

$\qquad$ _________________________

❒ Length of Rectangle = 5x = 5×5 = 25m

❒ Breadth of Rectangle = 4x = 4×5 = 20m

$\qquad$ _________________________

Now, using

⟹ Perimeter of Rectangle = 2(l+b)

where,

• Length, l = 25m
• Breadth, b = 20m

❆ Substituting these values ❆

➻ Perimeter of Rectangle = 2(l+b)

➻ Perimeter of Rectangle = 2(25+20)

➻ Perimeter of Rectangle = 2(45)

➻ Perimeter of Rectangle = 90m

Hence, the perimeter of the Rectangular plot is 90m