Please help with this problem!

Brandon wishes to fence in a rectangular area of his lawn for his rabbit. If the measure, in feet, of each side of the enclosure is a positive integer and the perimeter of the enclosure is 70 feet, what is positive difference between the area of the largest possible enclosure and the area of the smallest possible enclosure he could build?

Thank you so much...AGAIN!! lol

[: I really appreciate your help!

So far I need help too. I have the problem solved to 20ft for width and 15ft for height which would help to solve the area(15×20=300). I have this same problem and I need help to find the smallest area. Would that be zero? I am clueless.

Idk

To solve this problem, we need to find the dimensions of the largest and smallest possible enclosures, and then calculate the difference between their areas.

Let's start by considering the formula for the perimeter of a rectangle: P = 2(L + W), where P is the perimeter, L is the length, and W is the width.

We know that the perimeter of the enclosure is 70 feet, so we can set up the equation: 70 = 2(L + W).

Since L and W are both positive integers, let's start by finding all possible factors of 70 that add up to an even number.

The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, and 70.

Now, we need to find pairs of factors that add up to an even number. The only pairs that meet this condition are: (5, 7) and (10, 10).

Using these pairs, we can calculate the dimensions of the enclosures:
For (5, 7):
Length = 5
Width = 7

For (10, 10):
Length = 10
Width = 10

Now, we can calculate the areas of both enclosures:
For (5, 7):
Area = Length x Width = 5 x 7 = 35 square feet

For (10, 10):
Area = Length x Width = 10 x 10 = 100 square feet

Finally, we can calculate the positive difference between the two areas:
Difference = 100 - 35 = 65 square feet

Therefore, the positive difference between the area of the largest possible enclosure and the area of the smallest possible enclosure he could build is 65 square feet.

this looks more like a logic problem

the largest rectangle for a given perimeter is a square.
so for a perimeter of 70 feet, each side of the square must be 70/4 = 17.5 feet, and the area is 306.25 feet^2

the smallest "enclosure" would have an area of zero, so 306.25 would be the difference.