the length of a rectangular flower bed is 7 feet less than 3 times its width. the area of the bed is 20 feet squared. find the dimensions of the flower bed.
To find the dimensions of the flower bed, we'll use the given information:
Let's say the width of the flower bed is "x" feet.
According to the problem, the length of the flower bed is 7 feet less than 3 times its width. So, the length can be expressed as 3x - 7.
The area of a rectangle is given by the formula: Area = Length * Width.
In this case, the area of the flower bed is given as 20 square feet. So, we can set up the equation:
20 = (3x - 7) * x
To solve this equation, we'll multiply the terms inside the parentheses:
20 = 3x^2 - 7x
Now, rearrange the equation to set it equal to zero:
3x^2 - 7x - 20 = 0
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring:
(3x + 5)(x - 4) = 0
Setting each factor equal to zero, we have:
3x + 5 = 0 or x - 4 = 0
Solving these equations gives us two possible values for x:
3x = -5 or x = 4
To find the dimensions of the flower bed, let's consider the positive value of x, since the width cannot be negative:
Since x = 4, the width of the flower bed is 4 feet.
Now, we can plug this value back into the expression for the length:
Length = 3x - 7
Length = 3(4) - 7
Length = 12 - 7
Length = 5
Therefore, the dimensions of the flower bed are: Width = 4 feet, Length = 5 feet.
w(3w-7) = 20
w=4
check: 4*(3*4-7) = 4*5 = 20