Problem
ALG-B1-M06-P005 Normalizing a ratio
#5
★☆☆☆☆ Level 1 of 5
Let \(a:b:c=2:3:5\). Find \(\frac{a^2+b^2+c^2}{ab+bc+ca}\).
Set \(a=2t\), \(b=3t\), \(c=5t\).
Since the expression is homogeneous, the factor \(t\) cancels. We get \(\frac{4t^2+9t^2+25t^2}{6t^2+15t^2+10t^2}=\frac{38}{31}\).
The student should see that the actual scale is irrelevant.