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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 cm2, find the length of solid in cm.

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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×b+b×h+l×h)
Given, total surface area of the cuboid =1216cm2
2(5a×4a+4a×2a+2a×5a)=1216cm2
76a2=1216
a=4

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


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