what are all the possible rectangles with whole-number sidelengths that have a perimeter of 10 units.

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+2W10=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=51+4=54+1=52+3=53+2=5So (L,W) possibilities are:(1,4),(4,1),(2,3),(3,2)That makes 4 possibilities.