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.

Hi!

Let the length, breath and height of the cuboid be *l*, *b* and *h* respectively.

Given, *l* + *b* + *h* = 19cm ...(1)

Length of diagonal of the cuboid =

Squaring on both sides, we get

*l* ^{2} + *b* ^{2} = *h* ^{2} = 121cm^{2} ...(2)

Now, (*l* + *b* + *h*)^{2} = *l* ^{2} + *b* ^{2} + *h* ^{2} + 2*lb* + 2*bh* + 2*hl*

∴ 2(*lb + bh + hl* ) = ( *l + b + h*)^{2} – (*l* ^{2} + *b* ^{2} + *h* ^{2})

*⇒ *2(*lb + bh + hl* ) = (19cm)^{2} – 121cm^{2} = 361cm^{2} – 121cm^{2} = 361cm^{2} – 121cm^{2} = 240cm^{2 }(Using(1) and (2))

Surface area of the cuboid = 2(*lb + bh + hl*) = 240cm^{2}

∴ Surface area of the cuboid is 240cm^{2}.

Cheers!