The length, width and height of a cuboid are in the ratio 10 : 17 : 14, and its total surface area is 1096 cm$$^2$$​. Find the length (in cm) of the cuboid.

Correct option is B

Given:

The length, width, and height of a cuboid are in the ratio 10:17:14.
Total surface area = 1096 cm²

Formula used:
Total surface area of a cuboid = 2 × (length × width + width × height + height × length)

Solution:

Let the length = 10x, width = 17x, and height = 14x.
Total surface area = 2 × (length × width + width × height + height × length)
1096 = 2 × [(10x × 17x) + (17x × 14x) + (14x × 10x)]
1096 = 2 × [170x² + 238x² + 140x²]
1096 = 2 × 548x²
1096 = 1096x²
x² = 1
x = 1

Length = 10x = 10$$\times1 =10$$ cm​