Pythagorean Theorem Word Problem

Question

I got confused on how to complete word problems involving the Pythagorean Theorem. I understand how to do it when it is not in word problem form, but this one confused me. Please review the problem and my work and tell me if I was correct or where I went wrong.

 

Problem:

A car drives 50 miles east and then 40 miles due north. How far is it from where it started? Draw a picture, label the information, and solve.

 

My work:

40²+50²=c²

1600+2500=c²

√4100 = √c²

 √4100=c

 

√4100= √25 x √164

√4100= 5 x √4 x √41

√4100= 10√41

Answer 1

Your work is correct - although personally I would factor 4100 into 41*100 instead of 25*164 to simplify the radical.  But what you did is right so that's a pretty minor issue.  

 

You are probably confused because you think this should be a multiple of a 3-4-5 right triangle.  But in this case the 50 is one of the legs of the triangle, not the hypotenuse, so it doesn't work out to be a nice Pythagorean triple where all the sides are integers.  

Answer 2

Your answer is correct.

 

The expression 10√41 yields 64.0 miles.