Question

The dimensions of a cuboid are in the ratio of 2:3:4 and its total surface area is 280m^2. Find the dimensions.​

Answer 1

Answer:

Answer:

Given :-

Ratio of length Breadth and height of cuboid = 2:3:4

TSA = 280 m²

To Find :-

Dimensions

Solution :-

We know that

TSA = 2(lb + bh + lh)

280 = 2(2x × 3x + 3x × 4x + 2x × 4x)

280 = 2(6x² + 12x² + 8x²)

280 = 2(26x²)

280 = 52x²

280/52 = x²

√5.3 = x

2.3 = x

Therefore,

Length = 2x = 2 × 2.3 = 4.6 m

Breadth = 3x = 3 × 2.3 = 6.9 m

Height = 4x = 4 × 2.3 = 9.2 m

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 =88m

2

⇒2(x×2x+2x×3x+x×3x)=88m

2

⇒22x

2

=88

⇒x=2

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