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The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the total surface area of the cuboid.

(a) 361 cm2

(b) 240 cm2

(c) 209 cm2

(d) 121 cm2

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Correct option is (b) 240 cm2

Given, l + b + h = 19cm

Length of the diagonal of cube = \(\sqrt{l^2 + b^2 + h^2​}\)

Given, length of the diagonal = 11 cm

\(\sqrt{l^2 + b^2 + h^2​}\) = 11 cm

⇒ l2 + b2 + c2 = 112 = 121

⇒ (l + b + h)2 − 2(lb + bh + lh) = 121

⇒ 192 − 2(lb + bh + lh) = 121

⇒ 2(lb + bh + lh) = 240

But 2(lb + bh + lh) is the total surface area of the cuboid. 

Hence, total surface area of the cuboid = 240 cm2

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