Final answer:
The length of the rectangle is 8 1/2 inches and the width is 4 inches.
Step-by-step explanation:
To find the length and width of the rectangle, we can set up an equation using the given information. The area of the rectangle is 45 square inches, so we have:
(x + 8)(2x + 3) = 45
Multiply the binomials:
2x^2 + 19x + 24 = 45
Subtract 45 from both sides:
2x^2 + 19x + 24 - 45 = 0
Simplify the equation:
2x^2 + 19x - 21 = 0
Factor the equation:
(2x - 1)(x + 21) = 0
Set each factor equal to zero and solve for x:
2x - 1 = 0 or x + 21 = 0
2x = 1 or x = -21 (we discard this solution since lengths cannot be negative)
x = 1/2
Now we can find the length and width:
Length = x + 8 = 1/2 + 8 = 8 1/2 inches
Width = 2x + 3 = 2(1/2) + 3 = 1 + 3 = 4 inches