Question

1. each of the five squares in the figure has a side length of 1. what is the length of the segment \\( \overline{ab} \\)? (adapted from 2008 math kangaroo problem, level 9 - 10, question #5)

a. 6
b. \\( 2\sqrt{5} \\)
c. \\( \sqrt{5}+\sqrt{2} \\)
d. \\( \sqrt{5} \\)
e. none of these

Explanation:

Step1: Determine the horizontal and vertical distances

The horizontal distance from \(A\) to \(B\) is \(4\) units and the vertical distance from \(A\) to \(B\) is \(2\) units.

Step2: Apply the Pythagorean theorem

According to the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 4\) and \(b=2\). So \(AB=\sqrt{4^{2}+2^{2}}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\)

Answer:

B. \(2\sqrt{5}\)