a:b::2:3 , b:c::4:5 find ( a^2 + c^2 ) / ( a^2 +b^2 ) = m/n
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a b
b c
=a×b:b×b:b×c
=2 3
4 5
=8:12:15 =a:b:c
(a^2+c^2)/(a^2+b^2) =m/n
=(8^2+15^2)/(8^2+12^2) =m/n
=(64+225)/(64+144) =m/n
=289/208 =m/n
m:n::289:208
b c
=a×b:b×b:b×c
=2 3
4 5
=8:12:15 =a:b:c
(a^2+c^2)/(a^2+b^2) =m/n
=(8^2+15^2)/(8^2+12^2) =m/n
=(64+225)/(64+144) =m/n
=289/208 =m/n
m:n::289:208
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