The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm.
Question:

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

Solution:

Let the length, breadth and height (or depth) of the cuboid be l cm, b cm and h cm, respectively.

∴ l + b + h = 19           …..(1)

Also,

Length of the diagonal = 11 cm

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

$\Rightarrow l^{2}+b^{2}+h^{2}=121$           ……(2)

Squaring (1), we get

(l + b + h)2 = 192

⇒ l2 + b2 + h+ 2(lb + bh + hl) = 361

⇒ 121 + 2(lb + bh + hl) = 361                      [Using (2)]

⇒ 2(lb + bh + hl) = 361 − 121 = 240 cm2

Thus, the surface area of the cuboid is 240 cm2.