Question

Wayne used the diagram to compute the distance from Ferris, to Dunlap, to Butte.FerrisDunlap20 miButteWhat distance did Wayne compute?What is the distance if Wayne travels directly from Ferris to Butte?How much shorter is the distance directly from Ferris to Butte than the distance Wayne found?15 mi

Answer 1

Given:

The distance Wayne computed is;

`\begin{gathered} Ferris\text{ to Dunlap}=15mi \\ Dunlap\text{ to Butte}=20mi \\ Distance\text{ from Ferris to Butte through Dunlap}=15+20 \\ Distance\text{ from Ferris to Butte through Dunlap}=35mi \end{gathered}`

Therefore, the distance Wayne computed is 35 miles.

If Wayne travels directly from Ferris to Butte;

`\begin{gathered} The\text{ distance from Ferris to Butte directly is represented by }x \\ To\text{ get the distance, we use the Pythagorean theorem.} \\ x^2=15^2+20^2 \\ x^2=225+400 \\ x^2=625 \\ x=√(625) \\ x=25mi \end{gathered}`

Therefore, the distance if Wayne travels directly from Ferris to Butte is 25 miles.

The distance if Wayne travels directly is shorter than the distance Wayne found.

It is shorter by;

`35-25=10mi`

Therefore, it is shorter by 10 miles if Wayne travels directly from Ferris to Butte.