The dimensions (length and width) of the poster are 6 inches and 2 inches
Represent the length with x and the width with y
From the question, we have the following parameters
x = 5 + 0.5y
Area, A = 12
The area of a rectangle is represented as:
A = xy
Substitute the known values in the above equation
(5 + 0.5y) * y = 12
Expand the bracket
5y + 0.5y^2 = 12
Multiply through by 2
10y + y^2 = 24
Rewrite as:
y^2 + 10y - 24 = 0
Expand
y^2 + 12y - 2y - 24 = 0
Factorize the expression
(y - 2)(y + 12) = 0
Solve for y
y = 2 or y = -12
The dimension cannot be negative.
So, we have
y = 2
Substitute y = 2 in x = 5 + 0.5y
x = 5 + 0.5 * 2
Evaluate
x = 6
Hence, the dimensions (length and width) of the poster are 6 inches and 2 inches
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