The length of a rectangle is two meters less than twice the width. If the area of the rectangle is 222 square meters, find the dimensions
since area = width*length,
w(2w-2) = 222
Now solve for w, and get the length.
To solve this problem, we need to use the given information about the relationship between the length and width of the rectangle, as well as the area.
Let's denote the width of the rectangle as "w" (in meters) and the length as "l" (also in meters).
From the given information, we know that the length of the rectangle is two meters less than twice the width. Mathematically, we can represent this relationship as:
l = 2w - 2
The area of a rectangle is calculated by multiplying its length by its width. In this case, we know that the area is 222 square meters. So, we can express this relationship using an equation as well:
A = l * w
Substituting the value of "l" from the first equation into the area equation, we have:
222 = (2w - 2) * w
Simplifying the equation, we now have a quadratic equation:
222 = 2w^2 - 2w
Setting the equation equal to zero to solve for the width, we get:
2w^2 - 2w - 222 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, the quadratic equation does not factor easily, so we'll use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values for a, b, and c from our equation:
a = 2, b = -2, c = -222
w = (-(-2) ± √((-2)^2 - 4 * 2 * (-222))) / (2 * 2)
Simplifying this equation further, we get:
w = (2 ± √(4 + 1776)) / 4
w = (2 ± √1780) / 4
Now, we can calculate the possible values for the width as:
w = (2 + √1780) / 4 ≈ 8.91
w = (2 - √1780) / 4 ≈ -0.565
Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is approximately 8.91 meters.
To find the length, we can substitute the value of the width back into the equation for the length:
l = 2w - 2
l = 2(8.91) - 2
l = 17.82 - 2
l ≈ 15.82
Therefore, the dimensions of the rectangle are approximately 15.82 meters by 8.91 meters.