Question

a new pipeline is being constructed to re - route its oil flow around the exterior of a national wildlife preserve. the plan showing the old pipeline and the new route is shown below. about how many extra miles will the oil flow once the new route is established? a 24 b 68 c 92 d 160

1. a rectangular piece of paper measures 10 centimeters wide by 17 centimeters long. what is the length of the papers diagonal to the nearest centimeter? a. 14 centimeters b. 17 centimeters c. 20 centimeters d. 27 centimeters

Explanation:

Step1: Find length of old pipeline

Use Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 32\) and \(b = 60\). So \(c=\sqrt{32^{2}+60^{2}}=\sqrt{1024 + 3600}=\sqrt{4624}=68\) miles.

Step2: Calculate extra miles

The new - route length is \(32 + 60=92\) miles. The extra miles is \(92-68 = 24\) miles.

for second part:

Step1: Apply Pythagorean theorem for rectangle

For a rectangle with length \(l = 17\) cm and width \(w = 10\) cm, the diagonal \(d\) of the rectangle is given by \(d=\sqrt{l^{2}+w^{2}}\).

Step2: Calculate diagonal length

\(d=\sqrt{17^{2}+10^{2}}=\sqrt{289 + 100}=\sqrt{389}\approx 20\) cm.

Answer:

A. 24