Question

pls help for 15 points asap Phil traveled with his family by car. They started their trip from Lexington to Louisville, driving directly west for 60 miles. They then turned North, driving to Indianapolis which is 100 miles from Lexington. Then, they turned to the West again, and drove to Decatur which which is 170 straight miles from Louisville. How many miles did they cover in total driving from Lexington to Decatur ?

Answer 1

Given that Phil traveled with his family by car. They started their trip from Lexington to Louisville, driving directly west for 60 miles.

So AB=60

They then turned North, driving to Indianapolis which is 100 miles from Lexington.

So AC=100

Then, they turned to the West again, and drove to Decatur which which is 170 straight miles from Louisville.

so BD=170

Now we have to find about how many miles did they cover in total driving from Lexington to Decatur.

That means we have to find length of (AB+BC+CD)

We can use Pythogorean theorem to find the values of BC and CD.

$BC=\sqrt{AC^2-AB^2}=\sqrt{100^2-60^2}=\sqrt{10000-3600}=\sqrt{6400}=80$

$CD=\sqrt{BD^2-BC^2}=\sqrt{170^2-80^2}=\sqrt{28900-6400}=\sqrt{22500}=150$

then (AB+BC+CD)=60+80+150= 290

Hence final answer is miles.