# The sum of the length,breadth and height of a cuboid is 38cm and the length of its diagonal is 22cm. Find the surface area of cuboid.

2
by mathbubble8

• Brainly User
2015-01-04T13:53:34+05:30
You have two equations,
,

Square both of them and subtract one from the other, you get,

Hence, Surface Area, S = 960 cm².
Thanks Jackie. But the answer provided in my book is 960 cm²
Oh am sorry. That was my mistake. Thanks a lot. :)
Happy to help :-)
But how did we get 2(lb+bh+hl)= 38²-22² ??
2015-01-04T14:05:14+05:30
Let length =l , breadth = b and height =h
ATQ  l+b+h= 38 cm                        (1)
and  √(l² +b² + h²) = 22 cm         (2)
Surface area of cuboid = 2(lh+ lb+ bh)
= (l+b+h)² - (l²+b²+h²)
= 38² -22²
= 960
Surface area of cuboid is 960 cm²

Can u explain???
cuboid has six faces. Opposite faces are equal. surface area of each face are- lb, bh and lh . so the total surface area = 2lb+2 bh+2 lh
So why did we put it as (l+b-h)² - (l²+b²+h²) ??
we know (l+b-h)²= l²+b²+h² + 2(lb+bh+lh) that gives 2(lb+bh+lh)=(l+b-h)² - (l²+b²+h²)
Okay. :)