$latex Given\ that\ 25{{x}^{2}}-20xy+4{{y}^{2}}=0.$

$latex Find\ the\ value\ of\ \frac{{3x}}{{4y}}$

$latex 25{{x}^{2}}-20xy+4{{y}^{2}}=0$

Factorize the algebraic expression using either the cross method or special algebraic product a^{2}-2ab+b^{2} = (a-b)^{2}.

$latex {{(5x-2y)}^{2}}=0$

Square root both sides of the equation.

$latex 5x-2y=0$

Manipulate the equation until the left side is left with x/y.

$latex 5x=2y$

$latex \frac{x}{y}=\frac{2}{5}$

Multiply both sides of the equation by 3/4.

$latex \frac{3}{4}\times \frac{x}{y}=\frac{3}{4}\times \frac{2}{5}$

$latex \frac{x}{y}=\frac{3}{{10}}$

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