Let's denote the width of the poster as 'w' (in inches).
According to the given information, the length of the poster is 10 more inches than three times its width. So, the length can be expressed as 3w + 10.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is given as 88 square inches:
Area = length * width
88 = (3w + 10) * w
To solve for the dimensions of the poster, we can rewrite this equation in quadratic form:
3w^2 + 10w - 88 = 0
Now, we can solve this quadratic equation. There are different methods to solve it, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula in this case.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 3, b = 10, and c = -88. Substituting these values into the quadratic formula, we get:
w = (-10 ± √(10^2 - 4 * 3 * -88)) / (2 * 3)
Simplifying further:
w = (-10 ± √(100 + 1056)) / 6
w = (-10 ± √1156) / 6
w = (-10 ± 34) / 6
Now, we can calculate the two possible values of 'w':
w₁ = (-10 + 34) / 6 = 24 / 6 = 4
w₂ = (-10 - 34) / 6 = -44 / 6 = -22/3 ≈ -7.33
Since the width of the poster cannot be negative, we discard the negative value.
Therefore, the width of the poster is 4 inches.
To find the length, we can substitute the value of 'w' into the expression for the length:
Length = 3w + 10 = 3 * 4 + 10 = 12 + 10 = 22 inches
Hence, the dimensions of the poster are length = 22 inches and width = 4 inches.