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Question

The length, breadth and height of a rectangular solid are in the ratio $$5 : 4 : 2$$. If the total surface area is $$1216$$ $$\displaystyle cm^{2}$$, find the length of solid in cm.


Solution

The rectangular solid is a cuboid.
Let the length of the cuboid $$ = 5a $$, breadth $$ = 4a $$, and height $$ = 2a $$

Total surface area of a cuboid of length $$l$$, breadth $$b$$ and height $$h$$ $$ = 2(l \times b + b \times h + l \times h) $$
Given, total surface area of the cuboid $$ = 1216  {cm}^{2}$$
$$ \Rightarrow 2(5a\times 4a + 4a\times 2a + 2a\times 5a) = 1216 {cm }^{ 2 } $$
$$\Rightarrow  76 {a}^{2} = 1216 $$
$$ \Rightarrow  a  = 4 $$

Hence, the length of the cuboid $$ = 5a = 20 $$ cm, breadth $$ = 4a  = 16 $$ cm, height $$ = 2a = 8 $$ cm 


Mathematics

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