the width (x) of the rectangle = 41 inches
Explanation:
let the width = x
twice the width = 2x
The length of a rectangle is 1 inch shorter than twice the width (x) = 2x - 1
length = 2x -1
Area of rectangle = length × breadth
area (y) = 3321 square inches
y = x × 2x - 1 = x(2x - 1)
3321 = 2x² - x
2x² - x - 3321 = 0
We use factorisation to find x:
a = 2, b = -1, c = -3321
a × c = 2(-3321) = -6642
The factors which gives -1 when we sum together but gives -6642 when we multiply together are -82 and +81
2x² -82x + 81x - 3321 = 0
2x(x - 41) + 81(x - 41) = 0
(2x + 81) (x - 41) = 0
(2x + 81) = 0 or (x - 41) = 0
2x + 81 = 0
2x = -81
x = -81/2 inches
(x - 41) = 0
x - 41 = 0
x = 41 inches
Since we can't have a negative number as the width, the width (x) of the rectangle = 41 inches
