The sum of length, breadth and depth of a cuboid is 12 cm and its diagonal is `5sqrt(2)` cm. Find its surface area.

Explanation

`l+b+h=12` ….(1)
and `sqrt(l^(2)+b^(2)+h^(2))=5sqrt(2)` ….(2)
Squaring eq. (2), we have
`l^(2)+b^(2)+h^(2)=(5sqrt(2))^(2)=50` …..(3)
Squaring eq. (1), we have
`(l+b+h)^(2)=(12)^(2)`
`rArr l^(2)+b^(2)+h^(2)+2(lb+bh+hl)=144`
`rArr 50+2(lb+bh+hl)=144`
`rArr 2(lb+bh+hl)=144-50=94`
`rArr` Surface area of cuboid `= 94 cm^(2)`