Question

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

Answer 1

Let's assume -

The length (L) = x meters

The breadth (B)= 2x meters

The height (H) = 3x meters

According to Question,

Total surface area of cuboid = 88m

⇒ 2(LB + BH + LH) = 88m

⇒ 2[(x × 2x) + (2x × 3x) + (x × 3x)] = 88

⇒ 2[2x² + 6x² + 3x²] = 88

⇒ 2[11x²] = 88

⇒ 11x² = 88 / 2

⇒ 11x² = 44

⇒ x² = 44 / 11

⇒ x² = 4

⇒ x = √4

⇒ x = 2

Required Measurements -

Length = x = 2 m

Breadth = 2x = 2(2) = 4 m

Height = 3x = 3(2) = 6 m

Hence, the length, breadth & height are 2meters, 4meters & 6meters respectively.

Hope it helps ツ

Answer 2

Let the length of the cuboid =x, breadth =2x, height =3x

Total surface area of a cuboid =2(l×b+b×h+l×h)

Given, total surface area of the cuboid =88m²

⇒2(x×2x+2x×3x+x×3x)=88m²

⇒22x² =88

⇒x=2

Hence,

the length of the cuboid =x=2m, breadth =2x=4m, height =3x=6m