Todays Quiz : Surface Area of a cuboid whose diagonal andsum of l, b and h is known : Brain Boost

Surface Area of a cuboid whose diagonal andsum of l, b and h is known

Q . The sum of the length, breadth and depth of a cuboid is 19cm and its diagonal is 5√5. Its surface area is :-

(a)    361 cm²

(b)   125 cm²

(c)    236 cm²

(d)   496 cm²

Solution:-

It is given that

l+b+h = 19 cm

l²+b²+h²= (5√5cm)² = 125cm²

And we need to find Surface area that is =  2(lb+bh+hl)

Now, (l+b+h) x (l+b+h) { or 19x19}

= l²+b²+h²+lb+bh+hl+lb+bh+hl

= l²+b²+h²+2(lb+bh+hl)

=125+2(lb+bh+hl)

Than means,

19x19 = 125+2(lb+bh+hl)

361-125=2(lb+bh+hl)

236cm²=2(lb+bh+hl)

236 cm² = Surface Area

That means the answer is (c)