Answer: The walking path around it.
Explanation:
Remember the Pythagorean's theorem, for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:
A^2 + B^2 = H^2
or
H = √(A^2 + B^2)
Here, A + B is the total distance for the path, while the hypotenuse is the distance for the bridge
Here we can see that:
A = 1170 ft
B = 520 ft
Then:
H = √( (520 ft)^2 + (1170 ft)^2) = 1280.4 ft
Now, let's compute the costs.
For the bridge, we know that each foot costs $11, then for 1280.4 ft the cost is:
Cost of the bridge = (1280.4)*$11 = $14,084.4
And for the walking path, the cost is $6 per foot, then the total cost of the path is:
Cost of the path = (520 ft + 1170 ft)*$6 = $10,140
We know that the bridge is preferred if it is within the range of $1500 for the path's cost.
This range is:
($10,140 - $1,500, $10,140 + $1,500) = ($8,640, $11,640)
Here we can see that the cost of the bridge does not belong to this range, (is higher) so the option we should recommend is the walking path around.