2005 AMC 8 Problems/Problem 7

Problem

Bill walks $\tfrac12$ mile south, then $\tfrac34$ mile east, and finally $\tfrac12$ mile south. How many miles is he, in a direct line, from his starting point?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 1\tfrac14\qquad\textbf{(C)}\ 1\tfrac12\qquad\textbf{(D)}\ 1\tfrac34\qquad\textbf{(E)}\ 2$

Solution

We have a right-angle triangle with sides $3/4$ and 1. We can divide the simple pythagorean theorem identity 3,4,5 by 4 to get 3/4, 1, 5/4. This shows us the answer is D.

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AJHSME/AMC 8 Problems and Solutions

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2005 AMC 8 Problems/Problem 7

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