Question

The sum of length, breadth and height of cuboid is 19 cm and length of its diagonal is 11 cm. Find the total surface area of cuboid

Answer 1

these is the answer

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Answer 2

Let,

length, breadth and height of cuboid be l , b and h respectively

and its diagonal be d

then,

l + b+ h = 19 cm   -----------equation (1)

and

d = 11 cm

also diagonal of cuboid, d  = $\sqrt{l^{2}+b^{2}+h^{2} }$

so,

$\sqrt{l^{2}+b^{2}+h^{2} } = 11 \\\\( on squaring both sides we will get )\\\\l^{2} +b^{2} +h^{2} = 121 -----(equation(2))$

as we know,

TSA of cuboid = 2 (lb + bh + lh )

NOW,

taking eqn (1)

l +b + h = 19

(squaring both sides)

(l+b+h)^2 = (19)^2

( using identity : (a+b+c)^2 = x^2 + y^2 + z^2 + 2 xy + 2yz + 2 zx = x^2 + y^2  + z^2 + 2 (xy + yz + zx)  we will get )

$l^{2} +b^{2} +h^{2} + 2 ( lb + bh + lh) = 361$

( using equation (2))

121 + 2 ( lb + bh + lh ) = 361

2 (lb +bh + lh ) = 361-121

2 ( lb + bh + lh ) = 240 cm^2

SO THE TSA OF CUBOID WILL BE 240 SQUARE CMS.