Answer 1

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