The length of a rectangle is 2ft less than 3 times the width. If the area is 65 ft. Find the dimension
anooooooooooooooooo
what are the factors of 65?
5 and 13
looks like they work
shi8t hol4e
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's start by assigning variables:
Let's say the width of the rectangle is "x" ft.
According to the problem, the length of the rectangle is 2 ft less than 3 times the width. So, the length can be represented as (3x - 2) ft.
We know that the area of a rectangle is given by the formula: Area = Length * Width.
Given that the area is 65 ft², we can set up the following equation:
65 = (3x - 2) * x
Now, we have a quadratic equation to solve. Let's simplify it:
65 = 3x² - 2x
To solve the equation, we need to move all the terms to one side, so the equation becomes:
3x² - 2x - 65 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In our equation, a = 3, b = -2, and c = -65.
Substituting these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)² - 4 * 3 * (-65))) / (2 * 3)
Simplifying further:
x = (2 ± √(4 + 780)) / 6
x = (2 ± √784) / 6
x = (2 ± 28) / 6
Now, we have two potential solutions for x:
x₁ = (2 + 28) / 6 = 30 / 6 = 5 ft
x₂ = (2 - 28) / 6 = -26 / 6 = -13/3 ft
However, since width cannot be negative, we disregard the negative solution, leaving us with:
x = 5 ft
Now that we know the width, we can find the length:
Length = 3x - 2 = 3 * 5 - 2 = 15 - 2 = 13 ft
Therefore, the dimensions of the rectangle are:
Width = 5 ft
Length = 13 ft