the length of a rectangular garden is 4m more than its width determine the gardens width if the area is 117m^2
w(w+4)=117
w^2+4w-117=0
w=(-4+-sqrt(16+4*117))/2
w=-2+-sqrt(4+117)=-2+11=9
length then is 13
width --- x
length --- x+4
solve for x
x(x+4) = 117
hint: the quadratic factors nicely.
Let's assume the width of the rectangular garden is "x" meters. According to the given information, the length of the garden would be "4m more than its width", so the length would be "x + 4" meters.
Now, we can use the formula to find the area of a rectangle, which is length multiplied by width:
Area = Length * Width
Substituting the values in the equation:
117m^2 = (x + 4)m * xm
To solve this equation and find the width, we can simplify it further:
117m^2 = x(x + 4)m
117m^2 = x^2 + 4x
Now, let's rearrange the equation to make it quadratic:
x^2 + 4x - 117 = 0
To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. However, factoring this equation might be difficult due to the large number (117). Therefore, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the quadratic formula:
x = (-4 ± √(4^2 - 4 * 1 * -117)) / (2 * 1)
x = (-4 ± √(16 + 468)) / 2
x = (-4 ± √484) / 2
x = (-4 ± 22) / 2
Now, we can solve for two possible values of x:
x1 = (-4 + 22) / 2 = 18 / 2 = 9
x2 = (-4 - 22) / 2 = -26 / 2 = -13
Since the width cannot be negative, the width of the rectangular garden is 9 meters.
To determine the width of the garden, we can follow these steps:
Step 1: Let's assume the width of the garden is x meters.
Step 2: According to the given information, the length of the garden is 4 meters more than its width. So, the length of the garden can be expressed as x + 4.
Step 3: The area of a rectangle is calculated by multiplying its length with its width.
Given that the area of the garden is 117 square meters, we have the equation:
Length × Width = Area
(x + 4) × x = 117
Step 4: Now, we can solve this equation to find the value of x (the width of the garden).
Expanding the equation, we get:
x^2 + 4x = 117
Rearranging the equation in standard quadratic form:
x^2 + 4x - 117 = 0
Step 5: We can factorize the quadratic equation. In this case, the factors will be (x + 13)(x - 9) = 0.
Setting each factor equal to zero, we have:
x + 13 = 0 or x - 9 = 0
Solving for x:
x = -13 or x = 9
Since the width cannot be negative, we discard x = -13.
Therefore, the width of the garden is 9 meters.