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].
![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].](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/untitled-1629394468.png)
Solution:
To know the length of the wood required for the rungs, we will use the formula of the sum of n terms Sₙ = n/2 [a + l] as they are in AP.
Given:
- Distance between the consecutive rungs = 25 cm
- Distance between the top and bottom rungs = 2 ½ m = 2 ½ × 100 cm
Total number of rungs = [Total length of the ladder / distance between the consecutive rungs] + 1
∴ 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 [length of the lowest rung is 45 cm]
- Last term, l = 25 [length of the topmost rung is 25 cm]
- Number of terms, n = 11 [Total number of rungs is calculated as 11]
Hence sum of n terms of the AP Series,
Sₙ = n/2 [a + l]
S₁₁ = 11/2 [45 + 25]
= 11/2 × 70
= 11 × 35
= 385
Therefore, the length of the wood required for the rungs is 385 cm.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 5
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? [Hint: number of rungs = 250 / 25 + 1]
Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.4 Question 3
Summary:
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 cm.
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