the length of a rectangle is 2 centimetres less than twice the width. the area of the rectangle is 180 square centimetres. find the length and width of the rectangle.

L W = 180

2W -L = 2

Solve for L and W
(2W -2)*W -180 = 0
2W^2 -2W -180 = 0
This is a factorabble quadratic equation.
(W^2 -W -90) = 0
(W -10)(W+9) = 0

W = 10 cm. Ignore the negative root (-9)
L = 180/W = 18

To find the length and width of the rectangle, we can use algebraic equations based on the given information.

Let's say the width of the rectangle is "w" cm.
According to the problem, the length of the rectangle is 2 centimeters less than twice the width. Therefore, the length can be expressed as 2w - 2 cm.

The area of a rectangle is given by multiplying its length and width, so we can set up the equation:

Area = Length * Width

Substituting the values:

180 = (2w - 2) * w

Now, let's solve this quadratic equation to find the width of the rectangle:

180 = 2w^2 - 2w

Rearranging the equation:

2w^2 - 2w - 180 = 0

Dividing the equation by 2 to simplify:

w^2 - w - 90 = 0

This equation can be factored as:

(w - 10)(w + 9) = 0

So, either w - 10 = 0 or w + 9 = 0

Solving these equations, we get two possible values for the width:

1. w - 10 = 0
w = 10 cm

2. w + 9 = 0
w = -9 cm (This is not possible in this case since width cannot be negative)

Therefore, the width of the rectangle is 10 cm.

Now, let's substitute this value back into the equation for the length:

Length = 2w - 2
= 2(10) - 2
= 20 - 2
= 18 cm

Thus, the length of the rectangle is 18 cm.

In summary, the length of the rectangle is 18 cm, and the width is 10 cm.