Rectangle's Area

hobbs1989

New member
Joined
Apr 15, 2008
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2
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?
 
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 lw\displaystyle lw where l stands for lenght and w stands for width
The perimeter P is 2w+2l\displaystyle 2w + 2l

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

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

now we can factorise this as follows

lw2l2w=0\displaystyle lw -2l - 2w = 0

(l2)(w2)4=0\displaystyle (l-2)(w-2) - 4 = 0

(l2)(w2)=4\displaystyle (l-2)(w-2) = 4

This should hopefully show you the answer required :)
 
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