**Introduction:**

In this question, we are given a scalene triangle and we need to determine the percentage increase in its area when the length of one of its sides is doubled.

**Explanation:**

Let's consider a scalene triangle with side lengths a, b, and c. The area of a scalene triangle can be calculated using Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, given by:

s = (a + b + c)/2

Now, let's say we double the length of one side of the triangle. Without loss of generality, let's assume we double side a. So, the new side lengths of the triangle become 2a, b, and c.

**Calculating the new area:**

To calculate the new area, we need to determine the new semi-perimeter and substitute it into the formula:

New semi-perimeter = (2a + b + c)/2 = (a + b + c) = s (since 2a = a)

New area = √(s(s-2a)(s-b)(s-c))

**Calculating the percentage increase:**

To determine the percentage increase in the area, we need to compare the new area with the original area and calculate the difference:

Difference in area = New area - Original area

Percentage increase = (Difference in area / Original area) * 100

Substituting the values, we have:

Difference in area = √(s(s-2a)(s-b)(s-c)) - √(s(s-a)(s-b)(s-c))

Percentage increase = ((√(s(s-2a)(s-b)(s-c)) - √(s(s-a)(s-b)(s-c))) / √(s(s-a)(s-b)(s-c))) * 100

Simplifying the expression, we get:

Percentage increase = ((√(s(s-2a)(s-b)(s-c)) - √(s(s-a)(s-b)(s-c))) / √(s(s-a)(s-b)(s-c))) * 100

Percentage increase = ((√(s(s-b)(s-c)) - √(s(s-a)(s-b)(s-c))) / √(s(s-a)(s-b)(s-c))) * 100

Since the sides of a scalene triangle are different, the expression (√(s(s-b)(s-c)) - √(s(s-a)(s-b)(s-c))) / √(s(s-a)(s-b)(s-c)) will be greater than zero. Therefore, the percentage increase will be positive.

**Conclusion:**

Hence, we can conclude that when the length of one side of a scalene triangle is doubled, the area of the triangle is increased by 100%.