The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram. The construction cost has been estimated at $110 per linear foot.Find the estimated cost for constructing the street. (North Blvd. is 9 mi and Main St. is 4 mi)(North Blvd is height and Main St is base)
$5,700,000
$5,700,000
To find the estimated cost for constructing the street, we need to calculate the length of the street that needs to be constructed.
Given that North Boulevard is 9 miles and Main Street is 4 miles, we can consider North Boulevard as the height (h) and Main Street as the base (b) of a right triangle.
Using the Pythagorean theorem, we can calculate the length of the street:
Length of the street = √(b² + h²)
Length of the street = √(4² + 9²)
Length of the street = √(16 + 81)
Length of the street = √97
Now, we can multiply the length of the street by the construction cost per linear foot:
Estimated cost for constructing the street = Length of the street × Construction cost per linear foot
Estimated cost for constructing the street = √97 × $110
To calculate this, you can use a calculator or an online calculator:
Estimated cost for constructing the street ≈ $110 × 9.848857802
Estimated cost for constructing the street ≈ $1,083.37
So, the estimated cost for constructing the street connecting Main Street and North Boulevard is approximately $1,083.37.