The width of a rectangle is 2ft less than the length. The area is 8ft^2.Find the length and the width.
The width is__ ft.
The length is __ ft.
The factors of 8 are:
8, 1
4, 2
I got the width is 2 and the length is 4
Right again!
To find the length and width of the rectangle, we can use the formula for the area of a rectangle, which is length multiplied by width.
Let's assume the length of the rectangle is x. According to the problem, the width is 2 feet less than the length. Therefore, the width would be (x - 2).
We can now form an equation for the area of the rectangle, which is 8 square feet:
x * (x - 2) = 8
To solve this equation, we can start by simplifying it:
x^2 - 2x = 8
Rearranging the equation:
x^2 - 2x - 8 = 0
Now, we can solve this quadratic equation. We can do this by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring:
(x - 4)(x + 2) = 0
This gives us two possible solutions:
x - 4 = 0 or x + 2 = 0
Solving for x:
x = 4 or x = -2
Since a length cannot be negative, we discard the x = -2 solution.
Hence, the length of the rectangle is 4 feet.
Now, we can find the width by substitute the value of x into the expression we set for the width:
Width = x - 2 = 4 - 2 = 2
Therefore, the width of the rectangle is 2 feet.
To summarize:
The width is 2 ft.
The length is 4 ft.