The length of a rectangle is 5 centimeters less than six times its width. its area is 14 square centimeters. find the dimensions of the rectangle.

The length is 2.2 centimetres   and the width is 6.5 centimetres

Step-by-step explanation:

Let l be the length of the rectangle and w be the width of the rectangle.

First we will write the statement mathematically

"the length of a rectangle is 5 centimetres less than six times its width" can be written as ;

l = 5 - 6w (1)

"its area is 14 square centimetres" can be written as;

l × w =  14 (2)

substitute equation (1) in equation (2)

(5-6w)w = 14

5w - 6w² = 14

The equation can be re-arrange as;

6w² - 5w -14=0

Using formular method to solve;

] = 6 b = -5   c = -14

x =- b ±√b² - 4ac   /2

x = -6  ±√25 + 336

x = -6± √361

x = -6±19/2

Either x = -6 + 19 or  x = -6 -19

x=  13/2   or   x = -25/2

There is no such thing as negative length, so we will take w = 13/2

w = 13/2

Substitute w = 13/2 in equation (2)

l × w = 14

l×13/2 = 14

13l / 2 = 14

multiply both-side by 2

13l = 28

Divide both-side by 13

l ≈ 2.2

Therefore,

The width = 13/2 = 6.5  and the length is 2.2