Let the other two sides of the triangle be a and b. Since the largest side is the hypotenuse, we have, by Pythagoras theorem,

${Hypotenuse}^2$ = $a^2$ +  $b^2$

${13}^2$ = $a^2$ + $b^2$^ = 169           ------------------- (I)

Now,

Sum of the areas of the three squares = ${\left(side\text{Â}of\text{Â}yellow\text{Â}square\right)}^2$ + ${\left(side\text{Â}of\text{Â}brownish\text{Â}square\right)}^2$  +

${\left(side\text{Â}of\text{Â}blue\text{Â}square\right)}^2$

Sum of the areas of the three squares =$a^2$  + $b^2$^ + ${13}^2$ = ${13}^2$ + ${13}^2$ (from (I))

Sum of the areas of the three squares = 169 + 169 = 338.