Question : If $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}$, what is the value of $(L + J)^2:(J +K)^2:(K +L)^2$?
Option 1: 25 : 16 : 9
Option 2: 64 : 25 : 81
Option 3: 49 : 81 : 62
Option 4: 49 : 81 : 64
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Correct Answer: 49 : 81 : 64
Solution : Given: $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}$ Let, $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}=x$ So, $J=4x,K=5x$ and $L=3x$ Now, $(L + J)^2:(J +K)^2:(K +L)^2$ = $(3x+4x)^2:(4x+5x)^2:(5x+3x)^2$ = $49x^2:81x^2:64x^2$ = 49 : 81 : 64 Hence, the correct answer is 49 : 81 : 64.
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