AMC8 1999

AMC8 1999 · Q5

AMC8 1999 · Q5. It mainly tests Arithmetic misc, Area & perimeter.

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?

一个长50英尺、宽10英尺的矩形花园被栅栏围住。为了使花园更大，同时使用相同的栅栏，将其形状改为正方形。这个变化使花园扩大了多少平方英尺？

(A) 100 100

(B) 200 200

(D) 400 400

(E) 500 500

Answer

Correct choice: (D)

正确答案：（D）

Solution

We need the same perimeter as a $60$ by $20$ rectangle, but the greatest area we can get. right now the perimeter is $160$. To get the greatest area while keeping a perimeter of $160$, the sides should all be $40$. that means an area of $1600$. Right now, the area is $20 \times 60$ which is $1200$. $1600-1200=400$ which is $\boxed{D}$.

我们需要与$60$乘$20$矩形相同周长的花园，但要获得最大面积。现在周长是$160$。为了在保持周长$160$的同时获得最大面积，各边应为$40$。这意味着面积为$1600$。现在面积是$20 \times 60$即$1200$。$1600-1200=400$即$\boxed{D}$。

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