The area of a rectangular field is x^2-x-72 m^2. The length of the field is x+8 m. What is the width of the field in meters?
divide x^2 - x - 72 by x+8
(x+8)(x - ?) = x^2 - x - 72
looks like the missing bracket must be (x-9)
the width is x-9
check by multiplying it back out
Well, let's find the width of the field using this algebraic riddle!
We know that the area of a rectangle is equal to its length multiplied by its width. So, in this case, we have the area of the field given as x^2-x-72 m^2, and the length of the field as x+8 m.
To find the width, we can divide the area by the length.
So, width = area / length = (x^2-x-72 m^2) / (x+8 m).
Now, since you want to find the width in meters, we need to simplify the expression and cancel out the units:
width = (x^2-x-72 m^2) / (x+8 m)
width = (x-9) m.
Voila! The width of the field is "x-9" meters.
To find the width of the rectangular field, we need to divide the area of the field by its length.
Let's start by factoring the area expression: x^2 - x - 72
The factors of -72 that add up to -1 are -9 and 8, so we can rewrite the expression as: (x - 9)(x + 8)
Now, we can set up the equation for the width of the field:
Width = Area ÷ Length
Width = (x^2 - x - 72) ÷ (x + 8)
Since we have factored the area expression, we can simplify the equation:
Width = [(x - 9)(x + 8)] ÷ (x + 8)
The (x + 8) term cancels out, leaving us with:
Width = x - 9
Therefore, the width of the field is x - 9 meters.
To find the width of the rectangular field in meters, we need to know the formula for the area of a rectangle, which is given by A = length × width.
Given that the area of the rectangular field is x^2 - x - 72 m^2, and the length is x + 8 m, we can substitute these values into the formula:
A = (x + 8) × width
Now, let's simplify the equation:
x^2 - x - 72 = x × width + 8 × width
To solve for the width, we need to isolate it on one side of the equation.
Let's bring all the terms involving width to one side:
x^2 - x - 72 - x × width = 8 × width
Next, let's factor out the common term 'width':
x^2 - x - 72 - width(x + 8) = 0
We can now solve for the width by factoring the quadratic equation:
(x - 9)(x + 8) - width(x + 8) = 0
(x - 9 - width)(x + 8) = 0
From this equation, we have two possibilities:
1) (x - 9) = 0, which means x = 9.
2) (x + 8) = 0, which means x = -8. However, negative values for the length or width of the field are not practical, so we ignore this solution.
Therefore, x = 9.
To find the width, we substitute x = 9 back into the equation:
x + 8 = 9 + 8 = 17
So, the width of the field is 17 meters.