SOLUTION: . Elizabeth starts at her house then runs 2 miles south. She then turns and runs 5 miles west. If she runs in a straight line back to her house, how much distance will she have

Algebra ->  Length-and-distance -> SOLUTION: . Elizabeth starts at her house then runs 2 miles south. She then turns and runs 5 miles west. If she runs in a straight line back to her house, how much distance will she have      Log On


   

Question 1200142: . Elizabeth starts at her house then
runs 2 miles south. She then turns
and runs 5 miles west. If she runs in a
straight line back to her house, how
much distance will she have covered
in total? Round your answer to the
nearest tenth of a mile.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the Pythagoras formula for the distance


    d = sqrt%282%5E2%2B5%5E2%29 = use your calculator.

That's all.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

a = distance she runs south = 2
b = distance she runs west = 5
c = distance from start to finish along a straight line

Drawing


Use the Pythagorean Theorem to determine c.

a%5E2+%2B+b%5E2+=+c%5E2

c+=+sqrt%28a%5E2%2Bb%5E2%29

c+=+sqrt%282%5E2%2B5%5E2%29

c+=+sqrt%284+%2B+25%29

c+=+sqrt%2829%29 This is the exact straight-line distance from start to finish.

c+=+5.38516 This is the approximate straight-line distance from start to finish.

When rounding to the nearest tenth, we get 5.4

Answer: 5.4 miles