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?
2 answers:
Answer:
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 $900-500=\boxed{\text{(D)}\ 400}$.
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.
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