Answer:
12 and 16.
Explanation:
Let both positive numbers be x and y.
3/4 = x/y....... equation 1
x² + y² = 400..... equation 2
From equation 1
3/4 = x/y
Cross multiply
3y = 4x
Divide both sides by 3
y = 4x/3
Substitute y = 4x/3 into equation 2
x² + y² = 400
x² + (4x/3)² = 400
x² + 16x²/9 = 400
Multiply through by 9
9x² + 16x² = 3600
25x² = 3600
Divide both sides by 25
x² = 3600/25
x² = 144
Take the square root of both sides
x = √144
x = 12
Substitute x = 12 into equation 1
3/4 = x/y
3/4 = 12/y
Cross multiply
3y = 12 x 4
3y = 48
Divide both sides by 3
y = 48/3
y = 16