Answer: 6 inches
Explanation:
Let's assume the original side length of the square is "x" inches.
After one side was lengthened by 2 inches, the new length of that side becomes "x + 2" inches.
After the other side was lengthened by 3 inches, the new length of that side becomes "x + 3" inches.
The area of the original square is given by: Area = x * x = x^2 square inches.
The area of the new shape (after lengthening the sides) is given by: Area = (x + 2) * (x + 3) = (x^2 + 5x + 6) square inches.
According to the problem, the area of the new shape is double the area of the original square. So, we can write the equation:
2 * (x^2) = x^2 + 5x + 6
Now, let's solve for "x" by simplifying the equation:
2x^2 = x^2 + 5x + 6
Subtract x^2 and 5x from both sides:
2x^2 - x^2 - 5x = 6
Simplify:
x^2 - 5x - 6 = 0
Now, we have a quadratic equation in standard form. To solve for "x," we can factor or use the quadratic formula. Factoring gives:
(x - 6)(x + 1) = 0
Setting each factor to zero and solving for "x":
x - 6 = 0 or x + 1 = 0
If x - 6 = 0, then x = 6.
If x + 1 = 0, then x = -1.
Since side lengths cannot be negative, the length of the original square is "x = 6 inches."