Question

A ladder has rungs 25 cm apart, (see Figure). 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 are `2 1/2`m apart, what is the length of the wood required for the rungs?

Answer 1

It is given that the top and bottom rungs are 250 cm apart and the gap between two consecutive rungs is 25 cm.
`therefore` number of rungs `= ((250)/(25) +1) = 11.`
The largest rung is 45 cm long the smallest one is 25 cm long.
It is given that the rungs are decreasing uniformly in length from 45 cm at the bottom to 25 cm at the top.
So, the lengths of the rungs form an AP with a = 45cm and l = length of 11th rung = 25cm.
`therefore ` length of the wood required to form 11 rungs
`= (n)/(2) (a +l) cm = (11)/(2) (45 + 25) cm = ((11)/(2) xx 70)`cm = 385 cm.
Hence, the required length of the wood to form these rungs is 3.85m.