If a + b = c and c= d, then a + b = d2
What property is this

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

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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?

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​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:

answer: its because of life

step-by-step explanation: i dont know

according to egenuity the answer is

step-by-step explanation:

d. 344.22