Answer:
26 inches
Explanation:
Area of rectangle
= length ×width
= (2x -1)(x +2)
= 2x(x) +2(2x) -1(x) -2 (expand)
= 2x² +4x -x -2
= 2x² +3x -2
Given that the area is 42 inches squared,
2x² +3x -2= 42
2x² +3x -2 -42= 0 (-42 on both sides)
2x² +3x -44= 0 (simplify)
(x -4)(2x +11)= 0 (factorise)
x -4= 0 or 2x +11= 0
x= 4 or 2x= -11
x= -11/2 (*reject)
Length of rectangle
= 2(4) -1
= 8 -1
= 7 inches
Width of rectangle
= 4 +2
= 6 inches
Perimeter of rectangle
= 2(width +length)
= 2(7 +6)
= 2(13)
= 26 inches
*We reject x= -11/2 because the length and the width of the rectangle would be a negative number, which is not possible.