Question

A cable is installed around two edges of the rectangular field that is 860 feet long and 340 feet wide, as shown below. Suppose the cable costs $2100 per foot to install. Round all answers to the nearest hundredth.
a. How much did it cost to run the cable along the two edges of the field?



b. How much would it have cost to run the cable along the diagonal?



c. How much money would have been saved if the cable were installed along the diagonal of the field instead of around the edges of the field?

Answer 1

Answer:

a. 2,520,000.00

b. $1,942,017.51

c. $577,982.49

Step-by-step explanation:

Distances in a Rectangle

a.

Running the cable along the edges of the field would need a total length of 860 ft + 340 ft = 1,200 ft of cable. The unit cost of the cable is $2,100 per foot, thus the cost of the total lenght of cable was 2,100*1,200= $2,520,000.

b. If the cable ran along the diagonal, the distance must be computed by

$D=\sqrt{x^2+y^2}$

where x = 860 ft and y = 340 ft, thus

$D=\sqrt{860^2+340^2}=924.77$

D = 924.77 ft. The cost of the cable would be 2,100*924.77= $1,942,017.51

c. The savings if the cable were installed along the diagonal of the field instead of around the edges of the field would be

$2,520,000 - $1,942,017.51 = $577,982.49