Respuesta :
The dimensions that would maximize the area enclosed by the fence is 30m × 60m.
Area of a rectangle:
- area = lw
where
l = length
w = width
Perimeter of a rectangle:
- perimeter = 2l + 2w
Therefore,
The corral uses the side of a barn as one of its sides, so the fencing is required on three sides of the rectangular region. Therefore,
perimeter = L + 2w
L + 2w = 120
L = 120 - 2w
area = Lw
area = (120 - 2w)w
area = 120w - 2w²
area = -2w² + 120w
We have a quadratic equation and it is parabolic. The leading coefficient is negative. Therefore, the parabola opens downward and the vertex is the maximum point.
The area is maximized at the vertex. Therefore,
To find the vertex, we need to have our quadratic equation in general form,
ax² + bx + c = 0
so a = -2, b = 120
w = -b / 2a
w = - 120 / 2 × -2
w = -120 / -4
w = 30
Therefore,
area = -2(30)² + 120(30)
area = 1800m²
Therefore, the maximum area we can enclose is 1800 m², the width is 30m, then the length will be 60 m because 60 × 30 = 1800 m².
learn more on quadratic equation here: https://brainly.com/question/10833349
