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.
X=width
X+4= length
X(x+4)=60
You will be factoring
Width=6
Step 1: Let's assume that the width of the rectangular garden is "x" yards.
Step 2: According to the given information, the length is 4 yards more than the width, so the length would be "x + 4" yards.
Step 3: The area of a rectangle is calculated by multiplying the length and the width. In this case, the area is 60 square yards, so we can set up the equation:
(x)(x + 4) = 60
Step 4: Multiplying the terms inside the parentheses, the equation becomes:
x^2 + 4x = 60
Step 5: Rearranging the equation to get it in standard form, we have:
x^2 + 4x - 60 = 0
Step 6: Factoring the quadratic equation or using the quadratic formula, we can solve for x.
The factored form of the equation is: (x + 10)(x - 6) = 0
Setting each factor to zero, we get two possible values for x: x + 10 = 0 and x - 6 = 0
Solving for x, we find that x = -10 and x = 6.
Since length and width cannot be negative, we discard the negative value, x = -10.
Step 7: Therefore, the width of the garden is 6 yards (x = 6).
Step 8: To find the length, we substitute the value of x into the length equation:
Length = x + 4
Length = 6 + 4
Length = 10 yards
So, the dimensions of the garden are Width = 6 yards and Length = 10 yards.
To find the dimensions of the garden, we can set up an equation based on the given information.
Let's assume the width of the garden is "x" yards. According to the problem, the length is 4 yards more than the width, so the length can be represented as "x + 4" yards.
The area of a rectangle is calculated by multiplying the length by the width. In this case, the area is given as 60 square yards. So, we can set up the equation:
Length * Width = Area
(x + 4) * x = 60
To solve this equation, we can simplify it:
x^2 + 4x = 60
Now we have a quadratic equation. To solve for "x," we can rearrange the equation and set it equal to zero:
x^2 + 4x - 60 = 0
Next, we can factor the quadratic equation:
(x + 10)(x - 6) = 0
From this, we have two possible solutions:
x + 10 = 0 -> x = -10 (Discard this solution since width cannot be negative)
x - 6 = 0 -> x = 6
Since the width cannot be negative, the width of the garden is 6 yards.
Now, we can find the length by using the equation we set up initially:
Length = Width + 4 = 6 + 4 = 10 yards
Therefore, the dimensions of the garden are 6 yards (width) and 10 yards (length).