The perimeter of a particliar rectangle is 24 inches. if the length and width are positive integers, how many disinct areas could the rectangle have.

6 distinct areas. hope this helps luv

Let's set one side a rectangle as x and the other distinct one as y.

The perimeter would be x+x+y+y=24, or 2x+2y=24. This can be simplified to x+y=12.

Since the area is xy, we just have to find how many combinations of positive integer numbers add up to 12.

1 and 11 (area of 11)
2 and 10 (area of 20)
3 and 9 (area of 27)
4 and 8 (area of 32)
5 and 7 (area of 35)
6 and 6 (area of 36)

That's it.

So, this rectangle could have 6 distinct areas.

Hope this helps!

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