1976 AHSME Problems/Problem 3

Problem 3

The sum of the distances from one vertex of a square with sides of length $2$ to the midpoints of each of the sides of the square is

$\textbf{(A) }2\sqrt{5}\qquad \textbf{(B) }2+\sqrt{3}\qquad \textbf{(C) }2+2\sqrt{3}\qquad \textbf{(D) }2+\sqrt{5}\qquad \textbf{(E) }2+2\sqrt{5}$

Solution

The lengths to the side are $1, \sqrt{2^2+1^2}, \sqrt{2^2+1^2}, 1$ , respectively. Therefore, the sum is $2+2\sqrt{5}\Rightarrow \textbf{(E)}$ .~MathJams

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1976 AHSME Problems/Problem 3

Problem 3

Solution