the Length breadth and the height of a box area in the ratio 3 ratio 2

1.	the Length breadth and the height of a box area in the ratio 3 ratio 2 ratio 1 and its surface area is 2662 metre square find its deamination
Answer» $\huge\mathbb{SOLUTION:-}$ Let the SIDE be x 3x ,2x and x And SURFACE area =2662sq.m .Now $\boxed{\sf{T.S.A\:of\: cuboid=2(lb+bh+lh)}}$ $\bf\underline{\red{According \:To\: Question:-}}$ $\sf\implies 2662=2(3x\times 2x+2x\times x+x\times 3x)\\ \\ \sf\implies \cancel{\dfrac{2662}{2}}= 6x{}^{2}+2x{}^{2}+3x{}^{2}\\ \\ \sf\implies 1331= 11x{}^{2}\\ \\ \sf\implies \cancel{\dfrac{1331}{11}}=x{}^{2}\\ \\ \sf\implies 121=x{}^{2}\\ \\ \sf\implies \sqrt{121}=x\\ \\ \sf\implies {\blue{x=11}}$ The value of x is 11 Now the SIDES of BOX $\sf\bullet 3\times 11= 33m\\ \\ \sf\bullet 2\times 11=22m\\ \\ \sf\bullet x=11m$ $\sf\underline{Sides\:of\:box= 33m\:22m\:11m}$

the Length breadth and the height of a box area in the ratio 3 ratio 2 ratio 1 and its surface area is 2662 metre square find its deamination

Answer»

$\huge\mathbb{SOLUTION:-}$

Let the SIDE be x
3x ,2x and x
And SURFACE area =2662sq.m

.Now

$\boxed{\sf{T.S.A\:of\: cuboid=2(lb+bh+lh)}}$

$\bf\underline{\red{According \:To\: Question:-}}$

$\sf\implies 2662=2(3x\times 2x+2x\times x+x\times 3x)\\ \\ \sf\implies \cancel{\dfrac{2662}{2}}= 6x{}^{2}+2x{}^{2}+3x{}^{2}\\ \\ \sf\implies 1331= 11x{}^{2}\\ \\ \sf\implies \cancel{\dfrac{1331}{11}}=x{}^{2}\\ \\ \sf\implies 121=x{}^{2}\\ \\ \sf\implies \sqrt{121}=x\\ \\ \sf\implies {\blue{x=11}}$