Question

the sum of length, breadth and height of a cubodial room is 26m. Length of its diagonal is 20m. find the total surface area of cuboid

Answer 1

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answer is 276 m^2


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Answer 2

The total surface area of cuboid is $276m^{2}.$

Step-by-step explanation:

Let  the length = l, breadth = b and height = h of a cubodial room

To find the total surface area of cuboid, 2(lb + bh + hl) = ?

According to question,

l + b + h = 26                                    ..... (1)

and,

The diagonal of cuboid room = $\sqrt{l^{2}+b^{2}+h^{2}} =20$

⇒ $l^{2}+b^{2}+h^{2}=400$    ..... (2)

We know that,

$(l+b+h)^{2} =l^{2} +b^{2} +h^{2} +2(lb+lh+bh)$

Using (1) and (2), we get

$(26)^{2} =400 +2(lb+lh+bh)$

⇒ $2(lb+lh+bh)=676-400=276$ $m^{2}$

Hence,  the total surface area of cuboid is $276m^{2}.$