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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