It is given that
Ratio of three numbers
![\[=\text{ }1/2:\text{ }1/3:\text{ }1/4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-53beb4a1ac52c12be63fdb8d1111b518_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} =\text{ }\left( 6:\text{ }4:\text{ }3 \right)/\text{ }12 \\ =\text{ }6:\text{ }4:\text{ }3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6732fba0a53e20bacf8cd4944a189131_l3.png "Rendered by QuickLaTeX.com")
Consider first number =
![\[6x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-447dfddb99f84119a38a8ac7bd13e327_l3.png "Rendered by QuickLaTeX.com")
Second number =
![\[4x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5fa1f4196c2eb8fd5428cc4e2291e3b6_l3.png "Rendered by QuickLaTeX.com")
Third number =
![\[3x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6b5e78c8463d018536e643bc542c7efb_l3.png "Rendered by QuickLaTeX.com")
So based on the condition
![\[\begin{array}{*{35}{l}} {{\left( 6x \right)}^{2}}~+\text{ }{{\left( 4x \right)}^{2}}~+\text{ }{{\left( 3x \right)}^{2}}~=\text{ }244 \\ 36{{x}^{2}}~+\text{ }16{{x}^{2}}~+\text{ }9{{x}^{2}}~=\text{ }244 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-01730cf1f53d691bcd12ef11b441de63_l3.png "Rendered by QuickLaTeX.com")
So we get
Here
First number
![\[=\text{ }6x\text{ }=\text{ }6\text{ }\times \text{ }2\text{ }=\text{ }12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-962a2ab82c20e7304b27806412ce8f12_l3.png "Rendered by QuickLaTeX.com")
Second number
![\[=\text{ }4x\text{ }=\text{ }4\text{ }\times \text{ }2\text{ }=\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7871899616fb21d307d38bbd5f7a601f_l3.png "Rendered by QuickLaTeX.com")
Third number
![\[=\text{ }3x\text{ }=\text{ }3\text{ }\times \text{ }2\text{ }=\text{ }6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d4f2a5c20d9285857122d81bd51043d2_l3.png "Rendered by QuickLaTeX.com")
Three numbers are in the ratio
![\[\mathbf{1}/\mathbf{2}:\text{ }\mathbf{1}/\mathbf{3}:\text{ }{\scriptscriptstyle 1\!/\!{ }_4}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ecc5a82f6509735898276f67ff1acf1_l3.png "Rendered by QuickLaTeX.com")
![\[244\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4f455f1075156401423fe18244443fec_l3.png "Rendered by QuickLaTeX.com")