5 Aaron wants to draw rectangles that each have an area of 36 square inches.

The length and width of each rectangle are whole numbers of inches.

Tell whether each statement about Aaron's rectangles is True or False

a. A rectangle can have a width of 3 inches.

True

b. A rectangle can have a length of 8 inches.

True

C. A rectangle can have a length of 18 inches and a width

of 2 inches.

True

False

False

False

d. A rectangle can have a width of 6 inches and a perimeter

that is less than 36 inches.

True

False

e. A rectangle can have a length of 9 inches, a width of

4 inches, and a perimeter equal to its area.

True

False

5 Aaron wants to draw rectangles that each have an area of 36 square inches.

The length and width of each rectangle are whole numbers of inches.

OK, we have Area=L*W where area is 36 and L and W are whole numbers, aka non-negative integers.

36=LW

a. A rectangle can have a width of 3 inches.

Sure, L=36/W = 36/3=12, a whole number. True

b. A rectangle can have a length of 8 inches.

W=36/L=36/8=9/2, not a whole number. False

C. A rectangle can have a length of 18 inches and a width of 2 inches.

Sure 18*2=36, our area. True

d. A rectangle can have a width of 6 inches and a perimeter

that is less than 36 inches.

L=36/6=6

It's a square, perimeter 6+6+6+6=24 which is of course less than 36

True

e. A rectangle can have a length of 9 inches, a width of 4 inches, and a perimeter equal to its area.

Perimeters can never really equal areas; they have different units. Let's just assume they mean they have the same number.

Area is 9*4=36, as desired. Perimeter is 9+4+9+4=26, not equal to its area.

False