MHB Find Width of Rectangle with 600yd2 and 140yd Fencing

[alllove]

A rectangular enclosure must have an area of at least 600 yd2. If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?
Select one:
A. 35 ≤ w ≤ 60
B. 10 ≤ w ≤ 35
C. 10 ≤ w ≤ 60
D. 0 ≤ w ≤ 10

 

[skeeter]

length, $L$ and width $(70-L)$

constraints ...

$70-L \le L$

$L(70-L) \ge 600$

see what you can do from here

 

[HOI]

Since the problem specifically asks about "w", the width, I would, instead, say that $(70- w)w\ge 600$.

Of course that's exactly the same as the inequality skeeter gave for L. There will be two solutions. It is the condition that "the width cannot exceed the length" that allows you to distinguish between them.

 

[kaliprasad]

Width being less than square root of 600 I see that it is less than 25 so I have only one candidate d to check and width 10 so length 60 meets the criteria and hence the answer