If frac{A}{3} = frac{B}{2} = frac{C}{5}, then | vedclass

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(C) Given that $\frac{A}{3} = \frac{B}{2} = \frac{C}{5} = k$ (where $k$ is a constant).Therefore,$A = 3k$,$B = 2k$,and $C = 5k$.We need to find the ra

Vedclass · Accepted Answer

$64 : 25 : 49$

Vedclass · Answer

(C) Given that $\frac{A}{3} = \frac{B}{2} = \frac{C}{5} = k$ (where $k$ is a constant).Therefore,$A = 3k$,$B = 2k$,and $C = 5k$.We need to find the ratio $(C+A)^{2} : (A+B)^{2} : (B+C)^{2}$.Substitute the values of $A, B,$ and $C$ in terms of $k$:$(C+A)^{2} = (5k + 3k)^{2} = (8k)^{2} = 64k^{2}$.$(A+B)^{2} = (3k + 2k)^{2} = (5k)^{2} = 25k^{2}$.$(B+C)^{2} = (2k + 5k)^{2} = (7k)^{2} = 49k^{2}$.Thus,the ratio is $64k^{2} : 25k^{2} : 49k^{2}$.Dividing by $k^{2}$,we get $64 : 25 : 49$.

If $\frac{A}{3} = \frac{B}{2} = \frac{C}{5},$ then what is the value of the ratio $(C+A)^{2} : (A+B)^{2} : (B+C)^{2} ?$

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