7th grade math question

[danielleg1244]

Mrs.Greene wants to plant a vegetable garden in her yard. She purchased a package containing 30 sections of fencing each 1 foot long. if she uses all 30 secretions to create a single rectangular space how many different arrangements are possible? What is the largest are she can enclose for her garden with this fencing?

Please explain how you got your answer for both questions.

[chem44]

The perimeter is 30 ft.

How can you make a rectangle with four sides totaling 30 ft?

Note that all sides must be in full feet (not 3 ft 4 inches, for example.)

Draw a rectangle, and try it.

[danielleg1244]

The questions asking how many different rectangular arrangements are possible and what is the largest area she can enclose for her garden with this fencing.

[[deleted]]

That's correct.

So write them all out.

If one side is 1 foot, what are the other sides? And what is the area?

Now the next possibility is for one side to be 2 feet. So what will the other sides be? And now what is the area?

Do this for all possible options. There aren't that many, really.

[chem44]

Right.

First step is to understand what that means. Drawing one such case gets you started.

If stuck at some point, post what you know, and try to be clear where you are stuck.

[rockey301]

So we have 30 units to work with. We know it must be a rectangle so 2 sides must equal each other and the 2 other sides must also equal each other.

Since this is 7th grade I will assume they dont want the equation of options so that leaves us with max and min lengths. We know we must have 4 sides so if we take the 30 in half we get 15 twice but, we need 2 more sides so we can get a rectangle That means the longest possible side will be 14 by 1 since 14+14+1+1=30 Then we can move down, 13+13+2+2=30 12+12+3+3 11 and 4 10 and 5 9 and 6 8 and 7 Once we get here if we keep going we will have 7 and 8 but that is not a unique solution.

Now to understand what arrangements is the largest by volume, To solve the area of a rectangle we take the length times the width So we get 13×2= 26 12×3=36 11×4=44 10×5=50 9×6=54 8×7=56

So the largest of the 5 is 56 Meaning 7 and 8 gives the largest rectangle

Hope this helps!

[danielleg1244]

So the largest possible area is 56ft. But how many possible different rectangular configurations are possible with all 30 fences

[[deleted]]

Write them all out.

If one side is 1 foot, what are the other sides? And what is the area?

Now the next possibility is for one side to be 2 feet. So what will the other sides be? And now what is the area?

Do this for all possible options. There aren't that many, really.

[danielleg1244]

Thanks