Question

A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?

Answer 1

The area of the rectangular garden is 50 x 10 = 500 square feet.

The perimeter of the rectangular garden is 50 + 50 + 10 +10 =120 feet.

The perimeter of the square also needs to be 120 because it is using the same amount of fence.

Divide 120 by 4 sides: 120/4 = 30

Each side of the square garden would need to be 30 feet.

The area of a square is Side^2, 30^2 = 900 square feet.

The square is 900 - 500 = 400 square feet more.

Answer 2

The garden is enlarged by about 400 sq. feet to change its shape from rectangle to square with the same fence.

What are the area and perimeter of a rectangle?

The rectangle has 4 sides. Opposite sides are parallel and are equal in measure. So, the opposite sides are length(l) and width(w).

The perimeter of the rectangle = 2(l + w) units

and

The area of the rectangle = l × w sq. units

What are the area and perimeter of a square?

The square has 4 sides. Opposite sides are parallel and all the sides have equal measure.

Consider the side of the square as 's' units, then

The perimeter of the square = 4s units

and

The area of the square = s² units

Calculation:

Given that,

A rectangular garden has

length l = 50 feet

width w = 10 feet

So, the perimeter of the rectangle  = 2(l + w)

⇒ 2(50 + 10)

⇒ 2 × 60

∴ perimeter = 120 feet

Thus, the rectangular garden requires 120 feet fence.

The area of the garden = l × w

⇒ 50 × 10

∴ area = 500 sq. feet

After enlarging the garden to a square-shaped:

It has the same length of fence 120 feet. So, we can write

4s = 120

⇒ s = 120/4

∴ s = 30 feet

Thus, the measure of the side of the square after enlarging and changing the shape of the garden is s = 30 feet.

Then, the area of the square = s²

⇒ (30)²

∴ area of the square = 900 sq. feet

So, the enlargen square feet = area of the garden after enlarging(rectangle) = area of the garden before enlarging(square)

⇒ 900 - 500

⇒ 400 sq. feet

∴ 400 sq. feet are required for enlarging the garden from a rectangle shape to a square shape.

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