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
