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The sum of length, breadth and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid. |
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Answer» It is given that l + b + h = 19cm ……. (1) Diagonal = √ (l2 + b2 + h2) = 11cm…….. (2) Squaring on both sides of equation (1) (l + b + h) 2 = 192 So we get (l2 + b2 + h2) + 2 (lb + bh + hl) = 361 …….. (3) Squaring on both sides of equation (2) l2 + b2 + h2 = 112 = 121 ……. (4) Substituting equation (4) in (3) 121 + 2 (lb + bh + hl) = 361 So we get 2 (lb + bh + hl) = 361 – 121 By subtraction 2 (lb + bh + hl) = 240 cm2 Therefore, the surface area of the cuboid = 240 cm2. |
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