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5. Consider the image below of a pasture at McDonald's Farm.
750 ft
45°
Part A: If McDonald wants to fence in the square pasture and barbed-wire
fencing costs $1.15 per foot, then determine the cost to fence in
the pasture.
Part B: If McDonald wants to cover the square pasture in fertilizer, then he
needs to determine the area of the pasture. What is the area of
the pasture to the nearest hundredth?

5 Consider The Image Below Of A Pasture At McDonalds Farm 750 Ft 45 Part A If McDonald Wants To Fence In The Square Pasture And Barbedwire Fencing Costs 115 Per class=

Answer :

Answer:

Step-by-step explanation:

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The area of the square pasture is given by the leg length of the right

triangle which is the same as the side length of the square.

Correct responses:

  • Part A: $2,439.5
  • Part B: 281, 250 ft.²

Method by which the above responses are obtained

Part A

The given triangular side is a right triangle.

Length of the hypotenuse and an acute angle of the right triangle are;

750 ft. and 45°

Therefore;

Leg length of the right triangle = Side length of the square

Leg length of the right triangle = 750 ft. × sin(45°) = 375·√2 ft.

Side length of the square pasture, s = 375·√2 ft.

Perimeter of the fence = 4 × 375·√2 ft. = 1500·√2 ft.

Cost per foot for fencing = $1.15

  • The cost to fence the square pasture = $1.15/ft. × 1,500·√2 ft. ≈ $2,439.5

Part B:

The area, A, of the square pasture is given by A = s²

Which gives;

A = (375·√2)² = 281,250

  • The area of the square pasture is A = 281,250 ft.²

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