Problem solving Geometric area

[einie101]

These 2 problems with their intro have stumped a number of local students. I am an ESL english teacher about 35 years removed from Math. STudents are supposed to show their work how they arrived at the answer but they don't even know where to start.


Thanks for any help

 

[Dr.Peterson]

If I were working with these students, I would first ask to see their work, so I could try to nudge them in the right direction without just telling the answer.

For the second problem (square shape), the first thing to do is to see that l = w, so the area is lw = w^2, and the length of fencing is 2w + l = 2w + w = 3w. What does w have to be to use up all the fencing (which clearly will give the largest area)? (Ask them that!) To finish, they'll have to convert to yards.

The first problem confuses me, because it asks about the length of fencing, but the answers refer to l, which is not the length of fencing but the length of the yard.

 

[LCKurtz]

I agree that the first part is poorly stated, even if you assume by "length of fencing" he means the long side [MATH]l[/MATH] of the playground. It doesn't state that you must use all the [MATH]200[/MATH] feet of fencing. If you ASSUME that, then answer D is correct. But if you can use less than all of the fence, then [MATH]60 \le l \le 140[/MATH], which is not offered as a possible solution would be correct. Given that the problem states he has up to [MATH]200[/MATH] feet of fence to use, I would assume that you could use less and the problem is very ambiguous.

 

[HallsofIvy]

Presumably you are putting the fence around the yard so that the length of the fence along that side is the same as the length of the yard.