Question

A ladder has rungs 25cm apart. The rungs decrease uniformly in length from 45cm at the bottom to 25cm 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?
hint.. Number of rungs=250/25+1

Hint

Answer 1

Distance between the starting rung and the top most rung = 250 cm

Number of rungs in 250 cm with spacing of 25 cm = 250/25 = 10

Including the bottom most rung the total number of rungs on the ladder = 11

The length of rungs is an Arithmetic progression/series.

Sum of lengths of all 11 rungs = (1st term + last term)/2  * number of rungs
                   = (45+25)/2 * 11 = 385 cm

Answer 2

Answer:

Step-by-step explanation:

Solution :-

It is given that the top and bottom rungs are 250 cm apart and the gaps between two consecutive rungs is 25 cm.

Therefore,

Number of rungs = (250/25 + 1) = 11

The largest rung is 45 cm long and 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 from an A.P. with a = 45 cm and l = length of 11th rung = 25 cm.

Therefore,

Length of the wood required to form 11 rungs

= n/2 (a + l) cm

= 11/2(45 + 25) cm

= 11/2 × 70

= 385 cm.

Hence, the required length of the wood to form these rungs is 3.85 m.