Question

In the rectangle shown below, the length is longer than its width w. List all the possible

whole number dimensions for the rectangle, and name the dimensions that give the smallest
perimeter.

Area is 40 m2

Answer 1

Answer: w can be 1,2,4,5

Explanation:

Let's recap the formula of Area:
Area = width x length = w x l
Area = 40 = w x l

The definition of a whole number: is a number without fractions; an integer such as 0, 1, 2, 3, 4, 5, 6,...

Let's start with 0. 0 times anything is equal to 0, so we cannot make 40 out of zero. Cross this out.

Next, let's try with 1:

a. 1x40 = 40

Then, applying the same concept to the rest we have these multiplications:

b. 2x20 = 40

c. 4x10 = 40

d. 5x8 = 40

e. 8x5 = 40

f. 10x4 = 40

g. 20x2 = 40

h. 40x1 = 40

Let's recap the formula of Perimeter:

P = 2 x (w + l)

So, we have the calculated perimeters (according to the above finding):
a. P= 2x(1+40)=82

b. P= 2x(2+20)=44

c. P= 2x(4+10)=28

d. P= 2x(5+8)=26

The below answers do not fit the [width < length]

e. P= 2x(8+5)=26 [not an answer]

f. P= 2x(10+4)=28 [not an answer]

g. P= 2x(20+2)=44 [not an answer]

h. P= 2x(40+1)=82 [not an answer]