Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

Answer 1

8 to 6

Answer 2

let the numbers be 4x and 3x.

(4x)^2 + (3x)^2 = 100
16x^2 + 9x^2 = 100
25x^2 = 100
x^2 = 4
x = 2

So, the numbers are 6 and 8.

Check: 6^2 + 8^2 = 36+64 = 100

Or, you could have thought first of the ubiquitous 3-4-5 triangle.