Question

if a,b,c,d are proportionals then show that a^2+b^2:c^2+d^2=b^2+d^2:a^2+c^2

Answer 1

Answer:

Step-by-step explanation:

a:b=c:d

Or, a:c=b:d

Let a:c=b:d=r

Or,a/c=b/d=r

Therefore a=cr, b=dr

Now (a^2+b^2)/(c^2+d^2)

={(cr)^2+(dr)^2}/(c^2+d^2)

=(c^2r^2+d^2r^2)/(c^2+d^2)

=r^2(c^2+d^2)/(c^2+d^2)

=r^2

=(a/c)^2 Or (b/d)^2