Question

colleen lives 28 miles due south of her parents house and 96 miles west of her grandparents house. on her birthday, colleen drove from her house to her parents house. from there, she drove in a straight line to her grandparents house and then back home. how far did colleen drive on her birthday?
square miles

Explanation:

Step1: Identify distances

Colleen's house to parents': 28 miles; parents' to grandparents': unknown; grandparents' to Colleen's: 96 miles.

Step2: Calculate parents' to grandparents'

Use Pythagorean theorem: $d = \sqrt{28^2 + 96^2} = \sqrt{784 + 9216} = \sqrt{10000} = 100$ miles.

Step3: Sum total distance

Total = 28 + 100 + 96 = 224? Wait correction: 28+100+96=224? No wait 28+100=128 +96=224? Wait no wait original: Colleen's house to parents (28), parents to grandparents (100), grandparents back home (96). 28+100+96=224? Wait wait wait 28+96=124 +100=224? Wait but wait 28²+96²=784+9216=10000 so sqrt is 100 correct. Then total is 28+100+96=224? Wait but wait did I misread? Let me check again: Colleen lives 28 miles south of parents, 96 miles west of grandparents. So parents' house is north of Colleen, grandparents' is east of Colleen. So triangle: Colleen (C), parents (P), grandparents (G). CP=28, CG=96, right angle at C. So PG=100. So path is C→P→G→C: 28+100+96=224. Yes. So answer is 224. Wait earlier miscalculation corrected.

Wait wait no wait 28+100+96=224 yes. So final answer 224.

Step1: List known distances

Colleen→parents: 28 miles; grandparents→Colleen:96 miles.

Step2: Compute parents→grandparents

Apply Pythagorean theorem: $d=\sqrt{28^2+96^2}=100$ miles.

Step3: Sum total distance

Total = 28+100+96=224 miles.

Answer:

240 miles