Question

the sum of length,breath and depth of a cuboid is 19 cm and length of its diagonal is 11cm. find the surface area of the cuboid.​

Answer 1

Answer:

240

Step-by-step explanation:

Length of diagonal of cuboid =

l

2

+b

2

+c

2

Surface area of cuboid =2(lb+bh+hl)

Assume -

⇒length=l

Breadth=b

Depth=h

Given eq (1) l+b+h=19

eq (2) length of diagonal =11

⇒

l

2

+b

2

+h

2

=11

Simplifying eq (2)

⇒l

2

+b

2

+h

2

=121

Taking (l+b+h)

2

=l

2

+b

2

+h

2

+2lb+2bh+2lh

substituting values

⇒(19)

2

=121+2(lb+bh+lh)

⇒361−121=2(lb+bh+lh)

⇒240=2(lb+bh+lh)

∴ Surface area of cuboid =240.