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

10 cm

step-by-step explanation:

if the polygon is a rectangle, then the perimeter is x+x+y+y. using the values that you gave, the perimeter is 3+3+2+2=10cm.