Question

1. The area of a square park is same as of a rectangular park. If the side of the square park is 80 m and the length of the rectangular park is 100 m, find the breadth of the rectangular park. Which figure encloses more perimeter

Answer 1

Answer:

1. The breadth of the rectangular park is 64 m.
2. Rectangular park encloses more perimeter.

Step-by-step explanation:

Given that:

• The area of a square park is same as of a rectangular park.
• The side of the square park is 80 m.
• The length of the rectangular park is 100 m.

To Find:

1. The breadth of the rectangular park.
2. Which figure encloses more perimeter?

Let us assume:

• The breadth of the rectangular park be x.

Formula used:

• Area of a square = (Side × Side)
• Area of a rectangle = (Length × Breadth)
• Perimeter of a square = (4 × Side)
• Perimeter of a rectangle = 2(Length + Breadth)

Finding the breadth of the rectangular park:

• According to the question.

Area of square park = Area of rectangular park

• Substituting the values.

⟼ (80 m × 80 m) = (100 m × x)

⟼ 6400 m² = 100 m × x

⟼ x × 100 m = 64 m × 100 m

• 100 m cancelled both sides.

⟼ x = 64 m

∴ The breadth of the rectangular park = 64 m

Finding the perimeter of square park:

• Perimeter of square park = (4 × 80 m)
• Perimeter of square park = 320 m

Finding the perimeter of rectangular park:

• Perimeter of rectangular park = 2(100 m + 64 m)
• Perimeter of rectangular park = 2 × 164 m
• Perimeter of rectangular park = 328 m

What we get:

• After finding the perimeter of square park and rectangular park we get that the perimeter of rectangular park is greater than that of square park.

Answer 2

Answer:

Given :-

Area of square = Area of rectangle

Side of Square = 80 m

Length of park = 100 m

To Find :-

Who encloses more Perimeter

Breadth

Solution :-

Side × side = Length × Breadth

80 × 80 = 100 × Breadth

6400 = 100 × Breadth

6400/100 = Breadth

64 = Breadth

Now

Perimeter of Rectangle = 2l + 2b

=> 2(l + b)

=> 2(100 + 64)

=> 2(164)

=> 328 cm

Now,

Perimeter of square = side × 4

=> 80 × 4

=> 320 cm

Therefore,

Perimeter of Rectangle is greater