Answer
Longest side = $ \frac{1}{\sqrt 2} $
Work Step by Step
In a 45°–45°–90° triangle, if each of the shorter side is 'x'. then as per Pythagorean theorem-
$longest side^{2}$ = $x^{2} + x^{2}$ = 2$x^{2}$
Therefore longest side = $x\sqrt 2$
Given that each of the shorter sides is $ \frac{1}{2}$
Hence longest side = $ \frac{1}{2} \times \sqrt 2$ = $ \frac{\sqrt 2}{\sqrt 2\times\sqrt 2} $
Longest side = $ \frac{1}{\sqrt 2} $
