# 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 bottom rungs are 2 ½ m apart, what is the length of the wood required for the rungs? [Hint: number of rungs = 250 / 25 + 1].

**Solution:**

To know the length of the wood required for the rungs, we will use the formula of the sum of n terms S_{n} = n/2 [a + l] as they are in AP.

Given:

- Distance between the rungs = 25 cm
- Distance between the top and bottom rungs = 2 ½ m = 2 ½ × 100 cm

∴ Total number of rungs = [2 ½ × 100] / 25 + 1 = (250/25) + 1 = 11

From the given Figure, we can observe that the lengths of the rungs decrease uniformly, hence we can conclude that they will be in an AP

The length of the wood required for the rungs equals the sum of all the terms of this A.P.

- First-term, a = 45
- Last term, l = 25
- Number of terms, n = 11

Hence Sum of n terms of the AP Series,

S_{n} = n/2 [a + l]

S_{11} = 11/2 [45 + 25]

= 11/2 × 70

= 11 × 35

= 385

Therefore, the length of the wood required for the rungs is 385 cm.

**Video Solution:**

## 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 bottom rungs are 2 ½ m apart, what is the length of the wood required for the rungs?

### Class 10 Maths NCERT Solutions - Chapter 5 Exercise 5.4 Question 3:

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 bottom rungs are 2 ½ m apart, what is the length of the wood required for the rungs?

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 ½ m apart, then the length of the wood required for the rungs is 385 m.