Question

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.

Answer 1

Hlo mate your solution

Answer 2

AnswEr:

Let the

• Length = l cm
• Breadth = b cm
• Height = h cm

respectively. Then,

$\qquad\tt\underline{l+b+h=19}$_____(i)

Now ,

$\qquad\text{Diagonal\:=11cm}$

$\implies \tt\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } = 11 \\ \\ \implies \tt {l}^{2} + {b}^{2} + {h}^{2} = 121$

____________ (ii)

$\underline\text{Now,}$

$\tt \: l + b + h = 19 \\ \\ \implies \tt(l + b + h) {}^{2} = {19}^{2} \\ \\ \implies \tt {l}^{2} + {b}^{2} + {h}^{2} + 2(lb + bh + hl) = 361 \\ \\ \implies \tt \: 121 + 2(lb + bh + hl) = 361 \\ \\ \implies \tt2(lb + bh + hl) = 240$

___________( using (ii) )

$\mathfrak\green{Hence,\:the\:surface\:area\:of\:the\:cuboid\:is\:240\:cm^2.}$

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