Question

the dimensions of cuboid are in the ratio 1:2:3 and it's total surface area is 88m, find the dimensions of the cuboid

Answer 1

here's your answer looking for

we know that

TOTAL SURFACE AREA OF CUBOID =

$2(lb + bh + hl)$

so, now
let the dimensions be x, 2x ,3x.

total surface area =. 2(lb+bh+hl)
$88 = 2(x \times 2x + 2x \times 3x + 3x \times x) \\ \\ 88 = 2(2 {x}^{2} + 6 {x}^{2} + 3 {x}^{2} ) \\ \\ 88 = 2(11 {x}^{2} ) \\ \\ 88 = 22 {x}^{2} \\ \\ {x}^{2} = 4 \\ \\ x = \sqrt{4} \\ \\ x = 2$
so,

dimensions are as follows:-

l= x = 2m

b= 2x= 2×2=4m

and,

h= 3x=3×2=6m

hope you are satisfied with my answer