The length of a rectangular garden is 4 yards more than its width. The area of the garden is 60 square yards. Find the dimensions of the garden.
x(x+4) = 60
x^2 + 4 x - 60 = 0
(x+10)(x-6) = 0
x = + 6
and x+4 = 10
Hmmm. 60=10*6
To find the dimensions of the garden, let's consider that the width of the garden is x yards.
According to the given information, the length of the garden is 4 yards more than its width. Therefore, the length can be written as x + 4 yards.
The formula for calculating the area of a rectangle is length multiplied by width. In this case, the area of the garden is given as 60 square yards. Therefore, we have the equation:
Area = Length * Width
60 = (x + 4) * x
Simplifying the equation:
60 = x^2 + 4x
Now, let's rearrange this equation into a quadratic equation:
x^2 + 4x - 60 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. In this case, let's use factoring to solve it:
(x + 10)(x - 6) = 0
Setting each factor to 0:
x + 10 = 0 or x - 6 = 0
Solving for x in each case:
x = -10 or x = 6
Since the width cannot be negative, we discard the solution x = -10. Therefore, the width of the garden is x = 6 yards.
To find the length, we substitute this value back into the equation for length:
Length = x + 4 = 6 + 4 = 10 yards
Hence, the dimensions of the garden are width = 6 yards and length = 10 yards.