Jim is setting up a rectangular dog run in
his backyard. He buys six 3-foot sections
of fencing and a 3-foot wide gate. What
are the dimensions of the dog run with
the greatest area in each situation?
a) Jim uses the yard fence for one side of
the dog run.
b) Jim uses the corner of the yard fence
for two sides of the dog run.
I see you'd rather keep posting this than actually work on it.
He has 7 sections of material to use.
(a) the dog run could be 3x15 (1x5 panels) or 6x9 (2x3 panels)
(b) 3x18 or 6x15 or 9x12
Now, was that so hard?
To find the dimensions of the dog run with the greatest area, we need to understand the problem and apply some math concepts.
a) Jim uses the yard fence for one side of the dog run:
In this situation, the dog run will have one side that is the length of the yard fence. Let's assume the length of the yard fence is L feet. We have six 3-foot sections of fencing, so Jim can use four of them to create the other three sides of the dog run.
To maximize the area, we need to make the dog run as square as possible. Therefore, the two remaining sides should be the same length. Let's call this length W feet.
So, the length (L) of the yard fence will be one side of the dog run, and W will be the other side. We can calculate the area of the dog run using the formula A = L * W.
b) Jim uses the corner of the yard fence for two sides of the dog run:
In this situation, the dog run will have two sides that are the lengths of the yard fence. Again, let's assume the length of the yard fence is L feet. We still have six 3-foot sections of fencing, but this time we need to use two of them to create the other two sides of the dog run.
Similar to situation a), we want to maximize the area by making the dog run as square as possible. So, the two remaining sides should be the same length, and we'll call this length W feet.
Now that we know the dimensions of the dog runs in both situations, we can find their respective areas for comparison.
Remember to consider that when calculating the area, we want to subtract the width of the gate from the lengths.
These steps will help you find the dimensions and areas of the dog runs with the greatest area in each situation.