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?

Question

Cheese

Mathematics

10 October, 11:58

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?

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Answers (2)

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Kenna Odonnell · 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.

Vernon · Answer 2

The perimeter of the rectangular garden is $2 (50+10) = 120$ feet. A square with this perimeter has sidelength $120/4=30$ feet. The area of the rectangular garden is $ (50) (10) = 500$ and the area of the square garden is $ (30) (30) = 900$, so the area increases by $900-500=/boxed{/text{ (D) } / 400}$.