The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

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Solution

L+b+h=19
√l²+b²+h²=11
squaring both sides
(√l²+b²+h²)²=11²
l²+b²+h²=121 ------------------1
l+b+h=19 (given)
squaring both sides
(l+b+h)²=19²
l²+b²+h²+2(lb+bh+hl)=361
121+2(lb+bh+hl)=361 ---------(from 1)
2(lb+bh+hl)=361-121
2(lb+bh+hl)=240
surface area= 240cm ²

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