Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88 sq.m. Find its dimensions.​

Answer 1

Answer:

2m,4m,6m

Step-by-step explanation:

let the dimentions be x , 2x , 3x  

So total surface area=2(lb+bh+lb)

                                    =  2(2x²+6x²+3x²)

                                    =22x²=88m²

                                      = x=2m

So the dimensions are : 2m,4m,6m

Answer 2

Answer: 2m × 4m × 6m

Explanation:

If l:b:h = 1:2:3 then taking k as proportionality constant we can write

l = k

b = 2k

h = 3k

Surface area of a cuboid = 2(lb + lh + bh) = 88 m²

⇒ lb + lh + bh = 44 m²

⇒ k(2k) + k(3k) + (2k)(3k) = 44 m²

⇒ 2k² + 3k² + 6k² = 11k² = 44 m²

⇒ k² = 4 m² ⇒ k = 2 m

l = 2 m

b = 2×2m = 4 m

h = 3×2m = 6 m

Hence the dimentions of the cuboid are 2m×4m×6m