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# An architect designs a room with a rectangular floor that meets the fo

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19 Jul 2018, 21:49
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Difficulty:

25% (medium)

Question Stats:

75% (02:02) correct 25% (02:19) wrong based on 20 sessions

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An architect designs a room with a rectangular floor that meets the following requirements:

1. The length is twice the width

2. The area is at least 400 square meters

3. The perimeter is no more than100 meters

If w is the width of the floor, in meters, which of the following must be true for w?

A. 15 ≤ w ≤ 20

B. 15 ≤ w ≤ √398

C. 16.66667 ≤ w ≤ 20

D. √200/3 ≤ w ≤ 25/2

E. √200 ≤ w ≤ 50/3

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An architect designs a room with a rectangular floor that meets the fo  [#permalink]

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19 Jul 2018, 23:33
Bunuel wrote:
An architect designs a room with a rectangular floor that meets the following requirements:

1. The length is twice the width

2. The area is at least 400 square meters

3. The perimeter is no more than100 meters

If w is the width of the floor, in meters, which of the following must be true for w?

A. 15 ≤ w ≤ 20

B. 15 ≤ w ≤ √398

C. 16.66667 ≤ w ≤ 20

D. √200/3 ≤ w ≤ 25/2

E. √200 ≤ w ≤ 50/3

From the question stem, we can deduce the following information

1. $$L = 2W$$ where $$L$$ - Length of the rectangular floor and $$W$$ - Width of the rectangular floor

2. $$Area = L*W = 2W*W = 2*W^2$$

$$2W^2 \ge 400$$ --> $$w^2 \ge 200$$. This is written as $$W \ge \sqrt{200}$$

3. The perimeter is no more than 100 meters -> $$2(L + W) \le 100$$

This would mean that $$2(2W + W) \le 100$$ or $$W \le \frac{50}{3}$$

Therefore, combining these statements, the final inequality is $$\sqrt{200} ≤ w ≤ \frac{50}{3}$$ (Option E)
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An architect designs a room with a rectangular floor that meets the fo &nbs [#permalink] 19 Jul 2018, 23:33
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