Final answer:
To find the dimensions of the rectangle, an equation is set up using the perimeter formula and the expressions for length and width are solved for y. Substituting y back into the length and width expressions should give the dimensions of the rectangle; however, the options provided don't match the calculated results.
Step-by-step explanation:
The question asks us to find the actual dimensions of a rectangle with a given perimeter and expressions for its length and width. First, we need to form an equation using the formula for the perimeter of the rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Given:
Length = (2y + 6) inches
Width = (y - 4) inches
Perimeter = 52 inches
We can write the equation:
52 = 2(2y + 6) + 2(y - 4)
Solving for y gives us:
52 = 4y + 12 + 2y - 8
52 = 6y + 4
48 = 6y
y = 8
Now we substitute y back into the expressions for length and width:
Length = 2(8) + 6 = 22 inches
Width = 8 - 4 = 4 inches
From the options provided, none directly reflect the dimensions calculated. This means an error has occurred in the calculation or options provided.