Question

plz.. answer immediately.

The sum of the length, breadth and the height of a cuboid is 5√3cm and length of its diagonal is 3√5cm.
Find the total surface area of the cuboid
(a) 30 sq.cm
(b) 20 sq .cm
(c) 15 sq.cm
(d) 18 sq.cm

Hints:
(i) Use suitable algebraic
Identity to find the LSA of
the cuboid.
(ii) l+b+h= 5√3 and
$l ^{2} + b ^{2} + h ^{2} = 3 \sqrt{5}$
(iii) Square the first equation
and evaluate 2(lb+ bh+ hl).

give explanations also
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Answer 1

Answer:

we have

l+b+h = 5√3 .... (I)

and (√l^2+b^2+h^2) = 3√5

i.e., l^2+b^2+h^2 = (3√5)^2 = 45 ..... (II)

since, total surface area of cuboid = 2(lb+bh+hl)

Now , using algebric identity

(l+b+h)^2 = l^2+b^2+h^2+2(lb+bh+hl)

i.e., (5√3)^2 = 45 + 2(lb+bh+hl) ....(using (I) & (II) )

i.e., 75 = 45 +2(lb+bh+hl)

i.e., 30 = 2(lb+bh+hl)