Problem: In ratio and proportion, if x/(y+z)=y/(z+x)=z/(x+y) then prove each ratio = 1/2 or -1 [ Calculator, Method and examples ]
Solution:
Your problem `->` In ratio and proportion, if x/(y+z)=y/(z+x)=z/(x+y) then prove each ratio = 1/2 or -1
Here `x/(y+z)=y/(z+x)=z/(x+y)`
Case-1 : If `x+y+z!=0`, then
Each ratio`=(x+y+z)/(y+z+z+x+x+y)`
`=(x+y+z)/(2y+2z+2x)`
`=(x+y+z)/(2*(y+z+x))`
Cancel the common factor `(x+y+z)`
`=1/2`
Case-2 : If `x+y+z=0`, then
`y+z=-x`
Then, the first ratio `=x/(y+z)`
`=x/(-x)`
Cancel the common factor `-x`
`=-1`
Hence, each ratio `=-1`.
Thus, the value of each ratio is `1/2` or `-1`.
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Solution provided by AtoZmath.com
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