Question

the dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m2.find the dimensions

Answer 1

Hey mate!!!


Let the dimensions be x, 2x and 3x

We know that surface area =
$2(lb + bh + lh)$
given surface area = 88
$2(lb + bh + lh) = 88 \\ 2( {x} \times 2x + 2x \times 3x + 3x \times x) = 88 \\ 2(2 {x}^{2} + {6x}^{2} + {3x}^{2} ) = 88 \\ 2 \times {11x}^{2} = 88 \\ 22 {x}^{2} = 88 \\ {x}^{2} = 88 \div 22 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ x = 2$
now x is 2
so 2x = 2 × 2 = 4
3x = 3 × 2 = 6

The dimensions are 2, 4 and 6


Hope it helps dear friend ☺️✌️

Answer 2

Surface are of a cuboid is 2lb+2bh+2hl
where, L = length
b = bradth
h = height
Let 1:2:3 = 1x,2x,3x
so, surface area = 2(x*2x)+2(2x*3x)+2(3x*x)=88
                         ⇒   4x²+12x²+6x²=88
                         ⇒   22x²=88
                         ⇒   x²= 88/22
                         ⇒    x=√4
                         ⇒    x=2
So, Length = 2m
      Breadth= 2*2= 4m
      Height = 3*2 = 6m
Hope it help.