Question

一个长 $50$ 英尺、宽 $10$ 英尺的长方形花园被栅栏围住。为了在使用同样栅栏的情况下扩大花园，花园改成正方形。面积增加了多少平方英尺？

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?

$100$

$200$

$300$

$400$

$500$

答案：D

知识点：周长面积

难度评级：770

解答：

当前栅栏长度为英尺。如果四条边都相等，那么每条边长为 $120 \div 4 = 30$ 英尺。因此正方形面积为 $30^2 = 900$ 平方英尺。原花园面积为 $50 \cdot 10 = 500$ 平方英尺。 $2(50 + 10) = 2 \cdot 60 = 120$

因此面积差是 $900 - 500 = 400$ 平方英尺。

所以正确答案是 D。

The current length of the fence is $2(50 + 10) = 2 \cdot 60 = 120$ feet. If all the sides become the same, then each side length is $120 \div 4 = 30$ feet. As such, the area of the square is then $30^2 = 900$ square feet. Note that the original area of the garden is $50 \cdot 10 = 500$ square feet.

Therefore, the difference is $900 - 500 = 400$ square feet.

Thus, D is the correct answer.

1999 AMC 8 第 5 题

答案：D

难度评级：770

解答：

其他年份的第 5 题