Question

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 1

$\huge\mathbb{SOLUTION:-}$

• 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

$\sf\bullet 3\times 11= 33m\\ \\ \sf\bullet 2\times 11=22m\\ \\ \sf\bullet x=11m$

$\sf\underline{Sides\:of\:box= 33m\:22m\:11m}$

Answer 2

✪ QUESTION:-

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 dimension.

.°. let the side is r.

.°. L =3r, b=2r ,h=r

✪ SOLUTION:-

formula:- T.S.A of cuboid = 2(lb+bh+lh)

.°. put values in formula ,

.°. 2662 = 2( 3r ×2r +2r ×r +r ×3r)

.°. 2662 = 2(6r² ×2r²+3r²)

.°. 2662= 2(11) × r²

.°. 2662 =22 ×r²

.°. r²= 2662÷22

.°. r =√121

.°. r =11cm.

.°. dimension of cuboid,

.°. length =3 r =3×11= 33m.

.°. breath = 2 r =2 ×11=22m.

.°. height = r = 11m.

.°. dimension of cuboid is 33m ×22m ×11m.