Tom wants to build a pen in his yard for his dog. He buys 800 ft of fencing. He concludes that he can only build a rectangle with sides of 300 ft and 100 ft.
That gives him an area of 30,000 square feet.
What about a square with sides of 200 feet?
200 * 200 = 40,000 square feet.
2l+2w=800
l+w=400
so he can build an infinite number of such rectangles as long as the length + width = 400
e.g.
1 by 399
2 by 398
3 by 397
...
.1 by 399.9
.01 by 399.99
etc if you allow sides with non-integer values.
To verify whether Tom can build a rectangle with sides of 300 ft and 100 ft using 800 ft of fencing, we can calculate the perimeter of the rectangle.
A rectangle has two pairs of equal sides. Let's assume the length of one pair of sides is 300 ft, and the length of the other pair is 100 ft.
The perimeter of a rectangle is calculated by adding all four sides together. In this case, the perimeter can be calculated as:
Perimeter = 300 + 300 + 100 + 100 = 800 ft.
Since the perimeter of the rectangle equals the amount of fencing that Tom has (800 ft), it is indeed possible for him to build a rectangle with sides of 300 ft and 100 ft using 800 ft of fencing.