Answer:
a). A = -2x² + 200x
b). Widths = 40 feet and 60 feet
Explanation:
It is given that length of the fencing material = 200 feet
a). Peg wants to cover the vegetable garden from three sides with the given fencing material.
If length of the garden = l
and width of the garden = x
l + x + x = 200
l + 2x = 200
l = (200 - 2x) feet
Therefore, area of the garden = Length × width
A =
A = -2x² + 200x
b). Foe A = 4800 square feet,
4800 = -2x² + 200x
2x² - 200x + 4800 = 0
x² - 100x + 2400 = 0
x² - 60x - 40x + 2400 = 0
x(x - 60) - 40(x - 60) = 0
(x - 60)(x - 40) = 0
x = 40, 60 feet
Therefore, widths of Peg's garden will be 40 feet and 60 feet.