Name: Debbie
Who is asking: Student
Level of the question: Secondary

Question: Geometry
A small square is constructed. Then a new square is made by increasing each side by 2 meters. The perimeter of the new square is 3 meters shorter than 5 times the length of one side of the original square. Find the dimension of the original square

 
Hi Debbie. Remember that a square has all sides the same length. That means its side length is one quarter its perimeter. We'll be using that.

Let's use some variable names:
P = the perimeter of the new square
p = the perimeter of the original square
S = the side length of the new square
s = the side length of the original square

You are told that
S = s + 2
and
P + 3 = 5s

and you want to find "s". So using the relationship between a square's side length and its perimeter (4S = P) we can see that we first substitute 4S for P in

P + 3 = 5s

and get

4S + 3 = 5s

Now we substitute S = s + 2 into that to get

4(s+2) + 3 = 5s

Now rearrange to solve for s.

Stephen La Rocque>