Answer:
Option C, [tex]46[/tex]
Step-by-step explanation:
Step 1: Distribute
Formula → [tex]A = l * w[/tex]
[tex]120 = (x+3) * (x-4)[/tex]
[tex]120 = (x*x)+(x*-4)+(3*x)+(3*-4)[/tex]
[tex]120 = x^2 - 4x + 3x - 12[/tex]
Step 2: Solve for x
[tex]120 - 120 = x^2 - x - 12 - 120[/tex]
[tex]0 = x^2 - x - 132[/tex]
[tex]0 = (x - 12)(x + 11)[/tex]
[tex]x = 12, -11[/tex]
Step 3: Determine the perimeter of the rectangle
[tex]P = 2(l + w)[/tex]
[tex]P = 2((12 + 3) + (12-4))[/tex]
[tex]P = 2(15 + 8)[/tex]
[tex]P = 2(23)[/tex]
[tex]P = 46[/tex]
Answer: Option C, [tex]46[/tex]
