Answer:
Your Answer is 11 inches by 2 inches
Step-by-step explanation:
Area of Rectangle: Area = Length * Width
Given information:
- Area = 22 in^2
- Length = 2x - 1
- Width = x - 4
Put that into the Formula.
Area = Length * Width
22 in^2 = (2x - 1) * (x - 4)
Solve.
22 in^2 = (2x - 1) * (x - 4)
[tex]22 = (2x^2 - 9x + 4)\\2x^2 - 9x - 18 = 0[/tex]
Factor it.
(2x^2 - 9x - 18) = 0
(2x + 3)(x-6) = 0
[tex]x=-\frac{3}{2} ,6[/tex]
Plug that into the Length and Width to find the actually Length and Width.
Length:
[tex]2x - 1\\2*-\frac{3}{2}-1\\ -3-1\\-4\\[/tex]
Width:
[tex]x - 4\\-\frac{3}{2}-4\\ -\frac{11}{2}[/tex]
Area = Length * Width
Area = - 4* -11/2
Area = 22
Length:
[tex]2x - 1\\2*6-1\\ 12-1\\11\\[/tex]
Width:
[tex]x- 4\\6-4\\ 2[/tex]
Area = Length * Width
Area = 11 * 2
Area = 22 in^2
