Question

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.

Answer 1

Answer:

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

Answer 2

Not sure if you are familiar with the quadratic equation, but see picture