Question

Ratio of the surface areas of two cubes is 36:49.find the ratio of their edges.

Answer 1

$Let \: x \:and \: y \: are \: edges \: of \: two \\Cubes \: respectively$

$Ratio \: of \: Surface \: Areas = 36 : 49\: (given)$

$\implies \frac{6x^{2}}{6y^{2}}= \frac{6^{2}}{7^{2}}$

$\boxed { \pink { Surface \:area \:of \: a\:cube = 6 \times (edge)^{2}}}$

$\implies \left(\frac{x}{y}\right)^{2} = \left(\frac{6}{7}\right)^{2}$

$\implies \frac{x}{y} = \frac{6}{7}$

$\implies x : y = 6 : 7$

Therefore.,

$\red { Ratio \: of \: edges \: of \: cubes }\green {= 6:7 }$

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