Questions: If construction costs are 150,000 per kilometer, find the cost of building the new road in the figure shown to the right. The cost of building the new road is (Round to the nearest dollar as needed.)

If construction costs are 150,000 per kilometer, find the cost of building the new road in the figure shown to the right. The cost of building the new road is (Round to the nearest dollar as needed.)
Transcript text: If construction costs are $150,000 per kilometer, find the cost of building the new road in the figure shown to the right. The cost of building the new road is $______ (Round to the nearest dollar as needed.)
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Solution

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Solution Steps

Step 1: Calculate the length of the new road

The figure shows a right triangle with legs of length 8,000 m and 4,000 m. The new road represents the hypotenuse. We can use the Pythagorean theorem to find the length of the new road:

$c^2 = a^2 + b^2$ $c = \sqrt{a^2 + b^2}$ $c = \sqrt{8000^2 + 4000^2}$ $c = \sqrt{64,000,000 + 16,000,000}$ $c = \sqrt{80,000,000}$ $c = 8944.27$ meters

Step 2: Convert the length to kilometers

Since the cost is given per kilometer, we need to convert the length of the road from meters to kilometers. $8944.27 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 8.94427 \text{ km}$

Step 3: Calculate the cost

The cost of building the new road is $150,000 per kilometer. Multiply the length of the road in kilometers by the cost per kilometer:

$8.94427 \text{ km} \times \$150,000/\text{km} = \$1,341,640.50$

Final Answer:

The cost of building the new road is $1,341,641.

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