Writing a better solution

[JJKD]

Hey guys,

Firstly, just to give context, I'm starting an OU degree in Autumn with Math as my first module. My math is questionable so I've been given a few practise papers to prepare myself and there are a few questions I just can't grasp, even with all the materials I've been given.

The Question:

Consider the following exam question and a student’s attempt at a solution.

''Anny wants to fence off an area in the middle of a field in order to
make an enclosure for some pigs. She has 200 metres of fencing
available. Should she make the fencing in the shape of a square or a
circle, in order to enclose the greatest area?''

Annie's solution:

200 = 2πr
= πr^2 = 3183.
200 = 4l
l^2 = 2500, so circle.

(a) Criticise the solution, explaining why it is difficult to follow.

(b) Write out a better solution.

Thanks
Jay

EDIT: Sorry if this is the wrong place to post! Like I said, my math is questionable so I'm even unsure about the topic title!

[Guest]

It's clear to me that Annie understanding of the problem is fine, and that therefore the only legitimate criticism of her solution pertains to its exposition.

Some people are under the mistaken impression that good mathematical writing consists of numbers and symbols and uses as few words as possible. Adding some English around the equations will make Annie's solution much more readable. Particularly critical is explaining what each variable used is intended to represent. I also isolated r and l before substituting them into the area equations and added units where appropriate.


A circle of perimeter 200m has a radius, r, satisfying
200m = 2πr
or r = 200m/(2π)
and an area given by [tex]A_{cir}= πr^2[/tex] or approximately 3183m^2.

A square of perimeter 200m has a side length, l, satisfying
200m = 4l
or l = 50m
and an area given by [tex]A_{sq}=l^2[/tex]= 2500m^2, so the circle has the greater area.