Questions: A highway whose primary directions are north/south is being constructed along the west coast of a region. At one point, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The figure shows a diagram of the path that they decide on and the measurements taken. If L=2 mi, what is the length of highway needed to go around the bay? The total length of the highway needed to go around the bay is about miles. (Do not round until the final answer. Then round to two decimal places as needed.)

A highway whose primary directions are north/south is being constructed along the west coast of a region. At one point, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The figure shows a diagram of the path that they decide on and the measurements taken. If L=2 mi, what is the length of highway needed to go around the bay? The total length of the highway needed to go around the bay is about miles. (Do not round until the final answer. Then round to two decimal places as needed.)
Transcript text: A highway whose primary directions are north/south is being constructed along the west coast of a region. At one point, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The figure shows a diagram of the path that they decide on and the measurements taken. If $\mathrm{L}=2 \mathrm{mi}$, what is the length of highway needed to go around the bay? The total length of the highway needed to go around the bay is about $\square$ miles. (Do not round until the final answer. Then round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculate the length of AE

The length of AE is equal to L, which is given as 2 miles.

Step 2: Calculate the length of BD

The length of BD is equal to L, which is given as 2 miles.

Step 3: Calculate the length of EC

The length of EC is given as 1/8 miles, which is 0.125 miles.

Step 4: Calculate the length of CD

The length of CD is given as 1/8 miles, which is 0.125 miles.

Step 5: Calculate the total length around the bay

The total length around the bay is AE + EC + CD + BD, which equals 2 + 0.125 + 0.125 + 2 = 4.25 miles.

Final Answer: The final answer is $\boxed{4.25}$

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