Question

The area of a rectangle is
`14ft^2`, and the length of the rectangle is
`3ft` less than twice the width. Find the dimensions of the rectangle.

Answer 1

Length= 2width-3

Width=x

Length=2x+3

X(2x-3)=14

x must equal 3.5

Length=4

Width=3.5

Answer 2

So, Width = 7/2 or 3.5

Length = 4

Explanation:

Area of rectangle = 14 ft^2

Let width of rectangle 2 = x

and Length of rectangle = 2x-3

Formula used for area of rectangle

Area = Length * Width

14 = (2x - 3) x

14 = 2x^2 - 3x

=> 2x^2 -3x -14 = 0

Solving the quadratic equation using factorization

-28 x^2 = -7x * -4x

2x^2 -7x + 4x -14 = 0

x (2x -7) +2(2x-7) = 0

(x+2) (2x-7) =0

=> x + 2 =0 and 2x -7 = 0

x = -2 and x = 7/2

Since width cannot be negative so, x= 7/2

Width= x = 7/2

Length = 2x -3 => 2(7/2) - 3

=> 7 -3

=> 4

So, Width = 7/2 or 3.5

Length = 4.