A ladder has rungs 25 cm apart.(see Fig. 5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs arem apart, what is the length of the wood required for the rungs?
[Hint : Number of rungs

Total distance between top and bottom rung = 2 m 50 cm

Distance between any two rungs = 25 cm




And it is also given that bottom most rungs is of 45 cm length and top most is of 25 cm length.

As it is given that the length of rungs decrease uniformly, it will for an AP with a = 25, a₁₁ = 45 and n = 11

d can be calculated as follows:

nth term of an AP is given by

a_n = a + (n - 1)d

a₁₁ = a + 10d

45 = 25 + 10d

10d = 45 – 25 = 20

d = 2

Total length of wood will be equal to the sum of 11 terms:

= 11[ 25 + (10)]

= 11 x 35

= 385 cm

Therefore, total wood required for rungs is equal to 385 m