If (x+y):(y+z):(z+x)=7:9:13 for positive reals x,y,z, find x:y:z?
Show answer & explanation
Correct answer: C
Explanation
given :
(x + y) : (y + z) : (z + x) = 7 : 9 : 13
According to the formula:
assume
x + y = 7k
y + z = 9k
z + x = 13k
(x + y) + (y + z) − (z + x)= 7k + 9k − 13k= 3k
2y = 3k
y = 3k/2
x = 7k − y
x = 7k − 3k/2
x = 11k/2
z = 9k − y
z = 9k − 3k/2
z = 15k/2
Therefore
x : y : z= 11k/2 : 3k/2 : 15k/2= 11 : 3 : 15