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

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New post 19 Jul 2018, 21:49
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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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New post 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   [#permalink] 19 Jul 2018, 23:33
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