Thread: Completing the Square Word Problem #2

Bob is building a fence around his farm. He has 120m of fencing to use to fence the farm. What are the dimensions of the maximum area Bob can enclose?

I've got absolutely no idea how to solve this question. What variables should I start off with and what should they represent?

Originally Posted by shadow6

Bob is building a fence around his farm. He has 120m of fencing to use to fence the farm. What are the dimensions of the maximum area Bob can enclose?

I've got absolutely no idea how to solve this question. What variables should I start off with and what should they represent?

the first step is to draw a diagram. i guess we can skip that here

the next step is to find your objective and constraint equations.

(i suppose you want a rectangular fence?) if so, let the length be x and the width be y.

since we have 120m of fencing, we have that 2x + 2y = 120 => x + y = 60 ....this is your constraint equation.

the area of the fence is given by

A = xy

this is your objective equation.


do you know what to do from here?

This is the part that begins to confuse me. Normally I would have something to substitute for my variables, but this time I've hardly got anything. How to I find the length and width?

Originally Posted by shadow6

This is the part that begins to confuse me. Normally I would have something to substitute for my variables, but this time I've hardly got anything. How to I find the length and width?

as always, solve for one variable in your constraint and plug it into the objective. in this case, you will get a quadratic expression for the area. you need to find its maximum value

x + y = 60
x = 60 - y
y = 60 - x

A = xy
A = (60 - y)(60 - x)

This look right so far?

Originally Posted by shadow6

x + y = 60
x = 60 - y
y = 60 - x

A = xy
A = (60 - y)(60 - x)

This look right so far?

no, i said solve for ONE variable using your constraint. the point is to get the objective equation in a single variable.

Correction: (60-w) x w

I completed the square for this problem and did my substitutions. My final response was; "the dimensions of the max area bob can enclose are 30m by 30m." This seem right? Also tyvm for the help. Only 2questions left after this one.

Originally Posted by shadow6

Correction: (60-w) x w

I completed the square for this problem and did my substitutions. My final response was; "the dimensions of the max area bob can enclose are 30m by 30m." This seem right? Also tyvm for the help. Only 2questions left after this one.

yes, 30 by 30 is right