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Question
If `a/b = c/d`, show that: `(a + b) : (c + d) = sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`
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Solution
Let `a/b = c/d = k` ...(Say)
`=>` a = bk, c = dk
L.H.S = `(a + b)/(c + d)`
= `(bk + b)/(dk + d)`
= `(b(k + 1))/(d(k + 1))`
= `b/d`
R.H.S = `sqrt(a^2 + b^2)/sqrt(c^2 + d^2)`
= `sqrt((bk)^2 + b^2)/sqrt((dk)^2 + d^2)`
= `sqrt(b^2(k^2 + 1))/sqrt(d^2(k^2 + 1))`
= `sqrt(b^2)/sqrt(d^2)`
= `b/d`
∴ L.H.S = R.H.S
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