Question

The length of the diagonal of a cuboid is 5√5cm and the sum of its length, breadth, height is 19cm.find its total surface area

Answer 1

actually
diagonal of cuboid =root (l^2+b^2+h^2)
5root5=root (l^2+b^2+h^2)
now squaring both side
125=l^2+b^2+h^2
now use formula
(a+b+c)^2=a^2+b^2+c^2+2 (ab+bc+ca)

(l+b+h)^2=l^2+b^2+h^2+2 (lb+bh+hl)
(19)^2=125+ total area of cuboid
total area of cuboid=361-125=236 cm^2

Answer 2

let dimensions of cuboid are
Length=l cm
Breadth=b cm
height=h cm
l+b+h= 19 cm ----(1)
diagonal = 5root5
root l^2+b^2+h^2=5root5
do the square both sides
l^2+b^2+h^2=125----(2)
do the square of equation(1)
l^2+b^2+h^2+2(lb+bh+lh)=361
125+2(lb+bh+lh)=361
2(lb+bh+lh)=361-125
therefore
total surface area=2(lb+bh+lh)=236 square cm