AMC8 2000

AMC8 2000 · Q16

AMC8 2000 · Q16. It mainly tests Linear equations, Area & perimeter.

In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?

为了让Mateen在他的矩形后院走一公里（1000米），他必须沿着长度走25次，或者沿着周长走10次。Mateen的后院面积有多少平方米？

(A) 40 40

(B) 200 200

(D) 500 500

(E) 1000 1000

Answer

Correct choice: (C)

正确答案：（C）

Solution

The length $L$ of the rectangle is $\frac{1000}{25}=40$ meters. The perimeter $P$ is $\frac{1000}{10}=100$ meters. Since $P_{rect} = 2L + 2W$, we plug values in to get: $100 = 2\cdot 40 + 2W$ $100 = 80 + 2W$ $2W = 20$ $W = 10$ meters Since $A_{rect} = LW$, the area is $40\cdot 10=400$ square meters or $\boxed{C}$.

矩形的长度$L=\frac{1000}{25}=40$米。周长$P=\frac{1000}{10}=100$米。因为$P_{rect}=2L+2W$，代入数值得： $100=2\cdot 40+2W$ $100=80+2W$ $2W=20$ $W=10$米因为$A_{rect}=LW$，面积为$40\cdot 10=400$平方米，即\boxed{C}。

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