The total surface area of a cuboid is 174 cm². If its length and breadth are 3 cm and 5 cm, respectively, then what is the ratio of its length to its height?

Correct option is B

Given:

Total surface area of the cuboid = 174 cm².

Length of the cuboid = 3 cm.

Breadth of the cuboid = 5 cm.

Formula Used:
The total surface area (TSA) of a cuboid is given by:

TSA = 2(lb + bh + hl)

Where:

l = length,

b = breadth,

h = height.

Solution:

174 = 2(15 + 5h + 3h)

174 = 2(15 + 8h)

174 = 30 + 16h

144 = 16h

h $$= \frac{144}{16}$$​= 9

So, the height h = 9 cm.

Now, the ratio of the length to the height is:

​$$\frac{l}{h} = \frac{3}{9} = \frac{1}{3}$$​