Answer :

Given: Sum of length, breadth and height of a cuboid is 19 cm.


Length of diagonal is 5 √ 5 cm.


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


l + b + h = 19cm – 1


Length of a diagonal in a cuboid is given by : √(l2 + b2 + h2)


√(l2 + b2 + h2) = 5√5 cm (l2 + b2 + h2) = (5√5)2 = 125 cm2 – 2


Surface area of Cuboid is: 2(lb + bh + hl)


On squaring eq – 1 on both sides


We get


(l + b + h)2 = 192


l2 + b2 + h2 + 2(lb + bh + hl) = 361 cm2


125+ 2(lb + bh + hl) = 361 ( from eq – 2)


2(lb + bh + hl) = 361 – 125 = 236 cm2


2(lb + bh + hl) = 236 cm2


That is, Surface area of the given Cuboid is 236cm2

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