Question

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is $5\sqrt{5}$ cm. Its surface area is
(a) 361 cm²
(b) 125 cm²
(c) 236 cm²
(d) 486 cm²

Answer 1

(c) 236 cm²
Let l, b and h be the length, breadth and height of the cuboid.
Then,

$$\begin{gathered} l+b+h=19 \\ \Rightarrow {\left(l+b+h\right)}^2={\left(19\right)}^2 \end{gathered}$$

Therefore,

$$\begin{gathered} \left(l^2+b^2+h^2\right)+2\left(lb+bh+lh\right)=361 \\ \Rightarrow {\left(5\sqrt{5}\right)}^2+2\left(lb+bh+lh\right)=361 \\ \Rightarrow 2\left(lb+bh+lh\right)=\left(361-125\right) \\ \Rightarrow 2\left(lb+bh+lh\right)=236{\text{cm}}^2 \end{gathered}$$

Hence, the surface area of the cuboid is $236{\text{cm}}^2$.