Question

If length+breadth+height=19 and diagonal is
$5 \sqrt{5}$
Find total surface area of cuboid.​

Answer 1

length + breadth + height = 19

diagonal = 5 $\sqrt{5$

Now the diagonal  of cuboid is given by $\sqrt{l^2 +b^2 +h^2}$

squaring on both sides

$l^2 +b^2 +h^2 = 125$

Surface area of cuboid formula is 2(lb +bh +hl)

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

       19 x 19  = 125 + 2 ( lb + bh +hl )

        361 - 125 = 236 = 2 ( lb + bh +hl )

               ( lb + bh +hl ) = 118 cm^2

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