Question

1. The city commission wants to construct a new street that connects Main Street and North Boulevard asshown in the diagram below. The construction cost has been estimated at $110 per linear foot. Find theestimated cost for constructing the street. (1 mile = 5280 ft) one legs is 9 mi and the base is 6 mi but the hypotenuse is ?.

Answer 1

EXPLANATION

Since we have that the cost per linear foot is $110, and by applying the Pytagorean Theorem, we can get the value of the new street as shown as follows:

$\text{Hypotenuse}^2=\text{shorter leg\textasciicircum{}2 + larger leg \textasciicircum{}2}$

Where shorter leg = 6 , larger leg = 9 and Hypotenuse = New Street

Substituting terms:

$New_{\text{ }}street^2_{\text{ }}=6^2+9^2$

Applying the square root to both sides:

$\text{New street}=\sqrt[]{117}$

Simplifying:

$\text{New stre}et=3\sqrt[]{13}=10.82\text{ miles}$

Representing the length in ft units:

$\text{New str}eet\text{ = 10.82 }\cdot\text{ }5280\text{ = }57129.6\text{ ft}$

Finally, the cost per linear foot will be:

$\text{New stre}et=57129,6\text{ ft }\cdot\text{ }110\text{ =6,284,256}$

The cost of the street will be of $6,284,256