Alandowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. what should be the lengths of the sides of the triangle? let x be the length of the base of the triangle. write the area as a function of x. [first write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]

The lengths of each side = 1 mile

The largest area = 1/4(√3) miles²

Step-by-step explanation:

∵ Th length of the base = x

∵ Perimeter of Δ = 3 miles

∵ The triangle is isosceles

∴ The length of the two equal sides = (3 - x)/2

∵ The height of the Δ is ⊥ to the base and bisect it

∴ h² = [(3 - x)/2]² - (x/2)² = (9 - 6x + x²)/4 - x²/4

∴ h² = 9/4 - 3/2 x + x²/4 - x²/4 = 9/4 - 3/2 x

∴ h = √(9/4 - 3/2 x) = √[(9 - 6x)/4] = 1/2[√(9 - 6x)]

∴ Area of the Δ = (1/2) (x) [1/2√(9 - 6x)]

∴ A = x/4 [√(9 - 6x) ]

∴

∵ The largest area of the given perimeter is the area

   of the equilateral triangle

∴ The length of each side = 3/3 = 1 mile

∴ The largest area = 1/4(√3) miles²

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step-by-step explanation:

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6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.