The sum of the length, breadth …

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

Given  l+b+h= 19cm

Squaring both sides

(l+b+h)²= 361

l²+b²+h²+2(lb+bh+hl)= 361      -(1)

Also, Length of the diagonal = \(d = { \sqrt{l^2+b^2+h^2}}\)= 11 cm

Squaring both sides , d²= l²+b²+h²

l²+b²+h²⁼ 121

Putting it in eqn (1)

121 + 2(lb+bh+hl)= 361

2(lb+bh+hl)= 361-121

Surface area of cuboid = 240 cm²

Ans. let length of cuboid = l

breadth of cuboid = b

height of cuboid = h

According to question

l + b + h = 19   ............ (1)

We Know 

Length of Diagonal of Cuboid = \({ \sqrt{ l^2+ b^2 + h^2}}\)

=> \({ \sqrt{ l^2+ b^2 + h^2}} = 11\)

Squaring both sides, we get 

=> \({ l^2+ b^2 + h^2} = 121\)    .......(2)

Also 

=> \(({ l+ b + h})^2 = {l^2 + b^2 +h^2 + 2lb + 2lh +2bh }\)

=> \( { 2(lb + lh +bh) } = {({ l+ b + h})^2 - {(l^2 + b^2 +h^2)}}\)

put values from (1) and (2), 

=> \( { 2(lb + lh +bh) } = 361 - 121 = 240\)   ....... (3)

Surface Area of Cuboid = \( { 2(lb + lh +bh) } \)

=> So Surface Area of Cuboid = 240 cm²