# The sum of length

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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