Answer:
6.115 inches.
Explanation:
We know that the area of a rectangle is given by the formula:
Area = length x width
Here, the length is given by x inches and the width is given by 4x + 3 inches.
So, we can write:
Area = x(4x + 3)
Given that the area of the rectangle is 240 sq in, we can write:
240 = x(4x + 3)
Simplifying this equation, we get:
4x^2 + 3x - 240 = 0
We can solve for x by factoring the quadratic equation, or by using the quadratic formula.
Using the quadratic formula, we get:
x = (-3 ± sqrt(3^2 - 4(4)(-240))) / (2(4))
x = (-3 ± sqrt(2913)) / 8
x = (-3 ± 53.92) / 8
x = -8.865 or x = 6.115
Since the length of a side cannot be negative, we reject the negative solution.
Therefore, the value of x is approximately 6.115 inches.