The length of a rectangle is 1 foot less than twice the width, and the area of the rectangle is 21 ft.². Find the dimensions of the rectangle
w (2w-1) = 21
2 w^2 - w - 21 = 0
(2 w -7)(w+3) = 0
w = 7/2 = 3.5
then L = 6
Mr. Yau uses 88m of fence to enclose 384m^2 of a rectangle plot of lawn. Find the dimensions of the lawn.
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume the width of the rectangle is "x" feet.
According to the given information, the length of the rectangle is 1 foot less than twice the width. Therefore, the length can be expressed as (2x - 1).
The area of the rectangle is given as 21 ft².
We can use the formula for the area of a rectangle: Area = Length × Width
Substituting the given values:
21 = (2x - 1) × x
Expanding the equation:
21 = 2x² - x
Rearranging the equation to the standard quadratic form:
2x² - x - 21 = 0
Now, we can solve the quadratic equation to find the dimensions of the rectangle.
Factoring the quadratic equation:
(2x + 7)(x - 3) = 0
Setting each factor equal to zero:
2x + 7 = 0 or x - 3 = 0
Solving for x:
2x = -7 or x = 3
x = -7/2 or x = 3
Since the width cannot be negative, we discard the solution x = -7/2.
Therefore, the width of the rectangle is 3 feet.
Substituting this value back into the equation for the length:
Length = 2x - 1
Length = 2(3) - 1
Length = 6 - 1
Length = 5
Hence, the dimensions of the rectangle are:
Width = 3 feet
Length = 5 feet
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume the width of the rectangle is 'w' feet.
According to the problem, the length of the rectangle is 1 foot less than twice the width, which can be expressed as (2w - 1) feet.
The formula for the area of a rectangle is: Area = length × width
Given that the area is 21 ft.², we can set up the equation as:
21 = (2w - 1) × w
Now, let's solve this equation to find the dimensions of the rectangle.
Expanding the equation:
21 = 2w² - w
Rearranging the equation:
2w² - w - 21 = 0
This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use factoring to solve it.
Factoring the quadratic equation:
(2w + 7)(w - 3) = 0
Setting each factor to zero:
2w + 7 = 0 or w - 3 = 0
Solving for 'w':
For 2w + 7 = 0:
2w = -7
w = -7/2
Since width can't be negative, we discard this solution.
For w - 3 = 0:
w = 3
So the width of the rectangle is 3 feet.
Using this value, we can find the length:
Length = 2w - 1
Length = 2(3) - 1
Length = 6 - 1
Length = 5
Therefore, the dimensions of the rectangle are:
Width = 3 feet
Length = 5 feet