Question

The length of a rectangle is 1 inch shorter than twice the width (x).Which is the width (x) when the area (y) = 3321 square inches?

Answer 1

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