A rectangle has a width of x + 2 and a length of 2x - 1, with an area of 42 inches squared. Find the perimeter of the rectangle

26 inches

Step-by-step 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.

a

b

d

step-by-step explanation: