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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, the breadth and the height of the solid.
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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 = 1216 cm2
⇒ 2(5a × 4a + 4a × 2a + 2a × 5a) = 1216 cm2
⇒ 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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