Question

A right triangle with sides in the ratio 3:4:5 has one side length of 60. What are the possible lengths of the other sides?

(My teacher asked for a "let x represent" statement here but I'm not sure how to do that... is there a way? If so, please, do tell~)

Answer 1

There was probably a diagram with the question, because we have to know which side corresponds with the side of length 60

I will assume that the new side of 60 corresponds with the side of 3
let the hypotenuse side of the new triangle be x
then x/5 = 60/3= 20
x = 100

another way is to label the new triangle
3x, 4x, and 5x, (notice 3x:4x:5x = 3:4:5)

Then depending on which side matches the 60, set the corresponding side to 60
e.g. the way I assumed:
3x = 60
x = 20
then the new triangle has sides
3(20), 4(20), and 5(20) or 60, 80, 100