Question

the Length breadth and height of a cuboid are in the ratio 4 :2:1 and its total surface area is
${1372m}^{2}$
. find the dimensions of the cuboid

Answer 1

Let the length = 4x
Let the breadth = 2x
Let the height = x

Total Surface Area = 2(lb + bh + lh)

1372 = 2[ (4x × 2x) + (2x × x) + (x × 4x)]

1372 = 2[ 8x² + 2x² + 4x²]

1372 = 2( 14x²)

1372 = 28x²

1372/28 = x²

49 = x²

x = 7

The length = 4x = 4(7) = 28 cm

The Breadth = 2x = 2(7) = 14 cm

The Height = x = 7 cm