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?

Answers 1

Answer:

thanks to google

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.