Rectangle's Area

[hobbs1989]

Question

There are only two rectangles whose sides are whole numbers and whose area and perimeters are the same number.
WhAt are they?

I have figured out one.

3x6
Area = 18
3+3+6+6= 18

I cannot figure out the other. Does anyone have any insight into this problem?

 

[Denis]

4 by 4 ; a square is a special rectangle.

 

[Vernon]

here's the algebra that should help you find the last one ( remember a square is a form of rectangle btw )

The area A is represented by \(\displaystyle lw\) where l stands for lenght and w stands for width
The perimeter P is \(\displaystyle 2w + 2l\)

since in this problem they both equal each other we can have;

\(\displaystyle 2w + 2l = lw\)

now we can factorise this as follows

\(\displaystyle lw -2l - 2w = 0\)

\(\displaystyle (l-2)(w-2) - 4 = 0\)

\(\displaystyle (l-2)(w-2) = 4\)

This should hopefully show you the answer required

 

[hobbs1989]

Thanks very much!