Question

The sum of the length,breadth and height of a cuboid is 38cm and the length of its diagonal is 22cm. Find the surface area of cuboid.

Answer 1

You have two equations,
$l+b+h=38$,
$\sqrt{l^{2}+b^{2}+h^{2}}=22.$
Square both of them and subtract one from the other, you get,
$2(lb+bh+hl)=38^{2}-22^{2}=960$
Hence, Surface Area, S = 960 cm².

Answer 2

Let length =l , breadth = b and height =h
ATQ  l+b+h= 38 cm                        (1)
     and  √(l² +b² + h²) = 22 cm         (2)
Surface area of cuboid = 2(lh+ lb+ bh)
                                  = (l+b+h)² - (l²+b²+h²)
                                  = 38² -22²
                                  = 960
Surface area of cuboid is 960 cm²