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.
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?
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