Question

What are all the possible rectangles with whole-number side

Answer 1

Answer:

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.

Step-by-step explanation:

The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.

We have that P=10, so 10=2L+2W.

10=2L+2W

10=2(L+W)  By factoring using the distributive property.

2(5)=2(L+W)  I factored 10 as 2(5).

If 2(5)=2(L+W), then 5=L+W.

Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.

I think they want natural numbers {1,2,3,4,...}.  This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.

So now looking for numbers from this set that satisfy: L+W=5.

L+W=5

1+4=5

4+1=5

2+3=5

3+2=5

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.