Word Problem

Question

If the length of each side of a square is decreased by 4 inches the perimeter of the new square is 10 inches more than half the pereimeter of the original square.  

Answer 1

Presumably you are looking for the side of the original square although you have not stated that.
Let s be the side of the original square.
The original square has perimeter 4s and half of it is 2s; half the original perimeter + 10 is 2s + 10.
The perimeter of the reduced square is 4(s-4).
Translating from English to math (equation):
4(s-4) = 2s + 10
4s - 16 = 2s + 10
2s = 26
s = 13

Presumably you are looking for the side of the original square although you have not stated that.

Let s be the side of the original square.

The original square has perimeter 4s and half of it is 2s; half the original perimeter + 10 is 2s + 10.

The perimeter of the reduced square is 4(s-4).

Translating from English to math (equation):

4(s-4) = 2s + 10

4s - 16 = 2s + 10

2s = 26

s = 13