the length ,breadth and height of a cuboid is 8m,6m and 4m.find it's diagonal.
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the length ,breadth and height of a cuboid is 8m,6m and 4m.find it's diagonal.
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Given :
To find :
The Length of the diagonal of the cuboid.
Solution :
We know the formula for length of the diagonal for a cuboid ,i.e,
[tex]\boxed{\bf{D = \sqrt{l^{2} + b^{2} + h^{2}}}}[/tex]
Where :
Now by using the formula for Diagonal of a cuboid and substituting the values in it, we get :
[tex]:\implies \bf{D = \sqrt{l^{2} + b^{2} + h^{2}}} \\ \\ \\ [/tex]
[tex]:\implies \bf{D = \sqrt{8^{2} + 6^{2} + 4^{2}}} \\ \\ \\ [/tex]
[tex]:\implies \bf{D = \sqrt{64 + 36 + 16}} \\ \\ \\ [/tex]
[tex]:\implies \bf{D = \sqrt{116}} \\ \\ \\ [/tex]
[tex]:\implies \bf{D = \sqrt{2 \times 2 \times 29}} \\ \\ \\ [/tex]
[tex]:\implies \bf{D = 2\sqrt{29}} \\ \\ \\ [/tex]
[tex]\boxed{\therefore \bf{D = 2\sqrt{29}}} \\ \\ \\ [/tex]
Hence the diagonal of the cuboid is 2√29 cm.
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