Verified answer

a/5 = b/4 = c/3 = K -> a = 5k, b = 4k, c = 3k

d² = a²+ b² + c² = (20√2)² = 800

d² = 25k² + 16k² + 9k² = 800

d² = 50k² = 800

k² = 800/50 = 16

k = 4

a = 5k = 20

b = 4k = 16

c = 3k = 12

pronto

a/5 = b/4 = c/3

a = 5b/4

c = 3b/4

d² = a² + b² + c²

(20√2)² = (5b/4)² + b² + (3b/4)²

800 = 25b²/16 + b² + 9b²/16

800 = 25b² + 16b² + 9b² / 16

800 (16) = 50b²

20² . (2) . 4² = 5² . (2) . b²

b² = 20² . 4² / 5²

b = 16

a = 5b/4

a = (5 . 16) / 4

a = 20

c = 3b/4

c = (3 . 16) / 4

c = 12

a = 20

b = 16

c = 12