Answer:
10 inches
Explanation:
Let x be the length of one side of the original square.
According to the question:
One side is shortened by 3 inches can be expressed as (x-3)
Another side was lengthened by 5 inches can be expressed as (x+5)
We know that:


Again, we know that
The area of the new square is 55 inches greater than half the area of the original square.
This can be expressed as:

Substituting value

Expanding the left side of the equation, we get



doing Criss cross multiplication

keeping x^2 in left side


We can solve for x using the quadratic formula:

Comparing above equation with

In this case, a = 1, b = 4, and c = -140.
Substituting these values into the quadratic formula, we get:



Taking positive

x = 10
Taking Negative

x = -14
Since length of sqaure is always positive.
Therefore, the length of a side of the original square is 10 inches.