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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 area of cuboid.

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240

{cm}^{2}

230

{cm}^{2}

220

{cm}^{2}

210

{cm}^{2}

answer is A.

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Detailed Solution

Suppose,
Length of cuboid = l
Breadth of cuboid = b
Height of cuboid = h
Now we know that,
Cuboid's surface area

= 2 (lb + bh + hl)

square units.
The diagonal of cuboid of length

d = \sqrt{l^{2} + b^{2} + h^{2}}

Given,

l + b + h = 19 cm

Length of diagonal = 11 cm
Also,

d = \sqrt{l^{2} + b^{2} + h^{2}} = 11

Squaring on both sides

l^{2} + b^{2} + h^{2} = 121

Now, we know that,

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (ab + bc + ca)

So,

\begin{matrix} (l + b + h)^{2} = l^{2} + b^{2} + h^{2} + 2 (lb + bh + hl) \\ 19^{2} = 121 + 2 (lb + bh + hl) \\ 361 - 121 = 2 (lb + bh + hl) \\ 2 (lb + bh + hl) = 240 \\ Surface area = 240 {cm}^{2} \end{matrix}

Hence, option 1 is correct.

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