Math, asked by tanurathor3492, 11 months ago

The length breadth and height of are in the ratio 5 ratio 3 ratio 2 and its total area is 3968 CM square find the dimension of cuboid

Answers

Answered by prachitanandini
4

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Answered by SANDHIVA1974
2

Given :

The length breadth and height of a cuboid are in the ratio 5:3:2 .

Total Surface Area is 3968 cm² .

To Find :

Dimensions of the cuboid .

Solution :

\longmapsto\tt{Let\:Length\:be=5x}

\longmapsto\tt{Let\:Breadth\:be=3x}

\longmapsto\tt{Let\:Height\:be=2x}

Using Formula :

\longmapsto\tt\boxed{S.A\:of\:Cuboid=2(lb+bh+hl)}

Putting Values :

\longmapsto\tt{3968=2(5x\times{3x}+3x\times{2x}+2x\times{5x})}

\longmapsto\tt{3968=2({15x}^{2}+{6x}^{2}+{10x}^{2})}

\longmapsto\tt{\cancel\dfrac{3968}{2}={31x}^{2}}

\longmapsto\tt{\cancel\dfrac{1984}{31}={x}^{2}}

\longmapsto\tt{\sqrt{64}=x}

\longmapsto\tt\bf{8=x}

Value of x is 8 .

Therefore :

\longmapsto\tt{Length\:of\:Cuboid=5(8)}

\longmapsto\tt\bf{40\:cm}

\longmapsto\tt{Breadth\:of\:Cuboid=3(8)}

\longmapsto\tt\bf{24\:cm}

\longmapsto\tt{Height\:of\:Cuboid=2(8)}

\longmapsto\tt\bf{16\:cm}

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