Answer
Each shorter side = 5
Work Step by Step
In a 45°–45°–90° triangle,let's assume that 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 longest side is $ 5\sqrt 2$
Hence
$x\sqrt 2$ = $ 5\sqrt 2$
Dividing both the sides by $\sqrt 2$
x = 5
Thus each shorter side = 5
