A rectangular garden has an area of 770m^2 and its length is 21 m longer than the width. What are the width and length of the garden, and how much fencing would be required to enclose the garden?
Let's assume that the width of the garden is x.
According to the problem, the length of the garden is 21m longer than the width, so the length is x+21.
The area of the garden is the product of its length and width, which is x(x+21) = 770.
To find the values of x, we can set up the equation:
x(x+21) = 770
x^2+21x = 770
x^2+21x-770 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation, we get:
(x+35)(x-14) = 0
Setting each factor to zero to solve for x, we get x+35=0 or x-14=0.
If x+35=0, then x is -35 which is not a valid solution for the width of a garden.
If x-14=0, then x is 14 which is a valid solution. So the width of the garden is 14m.
The length of the garden is x+21 = 14+21 = 35m.
The perimeter of a rectangular garden is given by the formula P=2(l+w).
So the perimeter of this garden is P = 2(14+35) = 2(49) = 98m.
Therefore, 98 meters of fencing would be required to enclose the garden.