Question

Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a
single cube whose diagonal is 12v3 cm. Find the edges of the three cubes.​

Answer 1

diagonal =

$\sqrt{} ({(\sqrt{2} a) }^{2} + {a}^{2} ) = 12 \sqrt{3}$

$squaring \: both \: sides \\ { (\sqrt{2})a }^{2} + {a}^{2} = 144 \times 3 \\( \sqrt{2} + 1) {a}^{2} = 144 \times 3 \\ {a }^{2} = 144 \times 3 \div ( \sqrt{2} + 1) \\ a = 13 \\ using \: a \: find \: edges \: of \: cubes \: using \\ \: following \: formula$

27x^3+64x^3+125x^3=13×13×13

edges are

3x,4x,and 5x

plssssssssss plssssssssss mark brainliest lot of work