Question

Jashayne used the diagram to compute the distance from Ferris, to Dunlap, to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Jashayne found?

Answer 1

The distance from Ferris, to Dunlap, to Butte is given by

15 mi + 20 mi = 35 mi

Now, let us find the direct distance from Ferris to Butte.

Since this is a right-angled triangle, we can apply the Pythagorean theorem.

$c^2=a^2+b^2$

Where a and b are the shorter sides and c is the longest side.

$\begin{gathered} c^2=15^2+20^2 \\ c^2=225^{}+400 \\ c^2=625 \\ c=\sqrt[]{625} \\ c=25\; mi \end{gathered}$

The direct distance from Ferris to Butte is 25 mi

The difference between the longer and the direct distance is given by

Difference = 35 mi - 25 mi = 10 mi

Therefore, the direct distance from Ferris to Butte is 10 mi shorter than the distance Jashayne found.