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neokeynesian
10-24-2004, 05:56 AM
Question:

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

The length is twice the width

The area is at least 400 square meters

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) 16⅔≤w≤20

d) √200/3≤w≤25/2 e) √200≤w≤50/3

awhig
10-24-2004, 06:02 AM
Question:

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

The length is twice the width

The area is at least 400 square meters

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) 16⅔≤w≤20

d) √200/3≤w≤25/2 e) √200≤w≤50/3

True.

Expalination: Let l , w represent length and width
then condition 1 says l = 2w
condition 2 : l*b >= 400
2*b ^2 >= 400
or b >= +200^0.5 or -200^0.5 {remove the latter root}

condition 3: 2(l + b ) <= 100
3*b <= 50
or b <= 50/3

thus 200^0.5 <= b <= 50/3

lmtuan
10-24-2004, 06:32 AM
Let w >0 be the width of the floor, in meters. Then, we have:
~/ the length of the floor is 2*w.
~/ the perimeter of the floor is 6*w.
~/ the area of the floor is 2*w^2.
From condition 2 & 3, we can infer that:
* 6*w <= 100. This supplies that w <= 50/3.
* 2*w^2 >= 400 or w^2 >= 200. We note that w>0. Thus, w>=sqrt(200).
Hence, we can conclude that sqrt(200) <= w <= 50/3.