Question

In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the minimum total length of the escalator

Answer 1

Give the dimension of the cube = 800 × 800 × 720

Minimum total length of the escalator:

Shape of the hall is cuboid

The path of the escalator is

From OA to AB to BC to CD

OE = 800

EA = `1/4 xx "Height of the building"`

EA = `1/4 xx 720` = 180

Since there are four steps for the escalator

∴ OA² = OE² + EA²

= 800² + 180²

= (40 × 20)² + (9 × 20)²

= 40² × 20² + 92 × 20²

= 20² (40² + 9²)

= 20² (1600 + 81)

= 20² × 1681

OA² = 20² × 41² 

OA = `sqrt(20^2 xx 41^2)`

= 20 × 41

= 820

Since ∆OAE ≡ ∆ABB’ ≡ ∆ BCC ≡ ∆CDD’

We have OA = AB = BC = CD

Total length of the escalator

= OA + AB + BC + CD

= 820 + 820 + 820 + 820

= 4 × 820

= 3280

Minimum length of the escalator = 3280 units