a:b=c:d⟹ab=cd
Letab=cd=k
⟹a=bkandc=dk
a2+b2c2+d2=b2k2+b2d2k2+d2
=b2(k2+1)d2(k2+1)
=b2d2
6.5K viewsView 8 Upvoters
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Chris Eddy, Recovering aero engineer
Answered September 6, 2015 · Author has 133 answers and 268.8K answer views
To visualize these answers picture one right triangle with legs a and b and another with corresponding legs c and d. Since a^2+b^2 is the square of the first hypotenuse and c^2+d^2 the second, the desired ratio R is simply (h1/h2)^2. The two triangles are similar (by SAS) so:
R = (h1/h2)^2 = (a/c)^2 = (b/d)^2
6.4K viewsView 7 Upvoters
Kaushik Sreenivas, studied at Maharishi Vidya Mandir, Hosur
Answered August 21, 2015
Originally Answered: If a:b=c: d then the value of (a^2+b^2) / (c^2+d^2) is?
this would be the answer
8K viewsView 12 Upvoters
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Aakash Bamne, Trying to write Code in strings of Startup
Answered August 24, 2015
a:b=c:d
=> (a/b) = (c/d)
=> (a/b)^2 = (c/d)^2
=>a^2/b^2 = c^2/d^2
=>(a^2/b^2) + 1 = (c^2/d^2) + 1
=>(a^2 + b^2)/b^2 = (c^2 + d^2)/d^2
=>(a^2 + b^2)/(c^2 + d^2) = b^2/d^2
5.4K viewsView 5 Upvoters
David Seed, MSc numerical maths
Answered September 2, 2015 · Author has 1.3K answers and 867.5K answer views
If a/b = c/d = z
Also b/d = a/c
Then a=bz c=dz
a^2+b^2 = b^2(1+z^2)
c^2+d^2 = d^2(1+z^2)
a^2+b^2 /
c^2+d^2 =
(b/d)^2 =(a/c)^2
8.7K viewsView 8 Upvoters
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Nkumar, B.sc(math) from Vidyasagar University
Answered September 28, 2018 · Author has 207 answers and 177.2K answer views
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
4.5K viewsView 1 Upvoter
Aarushi Kalra, Investment consultant (2018-present)
Answered February 18, 2019
Since abcd are in proportion
Product of extreme =product of mean
ad=bc
Or a/b=c/d=k
Now a^2+b^2=b^2k^2+b^2= b^2(k^2+1)
c^2+d^2= d^2k^2+d^2=d^2(k^2+1)
Now a^2+b^2/ c^2+d^2= b^2(k^2+1)/d^2(k^2+1)
=b^2/d^2 ans
1.7K views
Abhi Jain
Answered August 21, 2015
Originally Answered: If a:b=c: d then the value of (a^2+b^2) / (c^2+d^2) is?
If a:b =c:d
squaring both sides , we will get
a^2:b^2 = c^2:d^2
Now apply componendo to the above equation:
a^2+b^2: b^2 = c^2+d^2 : d^2
Hence
a^2+b^2 / c^2+d^2 = d^2/b^2 = a^/c^2
1.5K views
Andrew Douglas Keyes, Did some math, I also touched a double bass
Answered October 9, 2020 · Author has 1.4K answers and 175.5K answer views
a2+b2c2+d2=b2d2(ab)2+1(cc)2+1=b2d2
46 views
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Step-by-step explanation:
