Question 1035557

Hi tutors, hopefully you ca help with this grade 3 math makes sense book word problem..:) 
The title: Comparing Area and Perimeter

Ingrid bought 12 units of fencing to enclose her yard.  What might the area of her yard be?
Give as many different answers as you can.
<pre>12 units represents the PERIMETER of the fence
As perimeter = 2 times length + 2 times width, we can say that:
P = 2(L + W)
12 = 2(L + W)
2(6) = 2(L + W)
2 = 2, so 6 = L + W, and therefore, {{{highlight_green(L = 6 - W)}}}. Choose any number for W (the width) and the length will be 6 minus that value. 
Multiply the width by the length and you have the area of the yard. 

<b><u>Choosing a value of 1 for width</b></u>
For example, if I choose 1 for the width, then the length is: 6 - 1 = 5, and the area is: 1(5), or {{{matrix(1,3, 5, square, units)}}}

<b><u>Choosing a value of 3 for width</b></u>
For example, if I choose 3 for the width, then the length is: 6 - 3 = 3, and the area is: 3(3), or {{{matrix(1,3, 9, square, units)}}}

<b><u>Choosing a value of 4 for width</b></u>
For example, if I choose 4 for the width, then the length is: 6 - 4 = 2, and the area is: 4(2), or {{{matrix(1,3, 8, square, units)}}}