The length of a rectangular garden is 4 yards more than the width. The area of the garden is 60 square yards. Find the dimensions of the garden.
Width = W yards.
Length = (W+4) yards.
A = (W+4)W = 60.
W^2 + 4W - 60 = 0
C = -60 = -6*10
(w-6)(w+10) = 0
W-6 = 0
W = 6
W+10 = 0
W = -10.
Use the positive value for W:
W = 6 Yds.
L = W+4 = 6+4 = 10 Yds.
To find the dimensions of the garden, we need to set up equations based on the given information.
Let's assume the width of the rectangular garden is x yards.
According to the first piece of information, the length is 4 yards more than the width. Therefore, the length would be (x + 4) yards.
The area of a rectangle is calculated by multiplying the length by the width. So, we can set up the following equation based on the second piece of information:
Area = Length × Width
60 = (x + 4) × x
Now, we can solve this equation to find the value of x, which represents the width of the garden:
60 = x^2 + 4x
Rearranging the equation:
x^2 + 4x - 60 = 0
This is a quadratic equation, so we can solve it by factoring or by using the quadratic formula.
By factoring, we can rewrite the equation as:
(x + 10)(x - 6) = 0
Now, set each factor equal to zero and solve:
x + 10 = 0 or x - 6 = 0
Solving for x in each equation:
x = -10 or x = 6
Since the width of a rectangle cannot be negative, we discard x = -10.
Therefore, the width of the garden is x = 6 yards.
Using the first piece of information, the length would be 6 + 4 = 10 yards.
So, the dimensions of the garden are width = 6 yards and length = 10 yards.