Find the total reduction in length over all the rungs. Find the difference in length between each rungs.
in NCERT Solution for class x math chapter 5 Arithmetic Progressions Solutions for Class 10th Maths, EXERCISE 5.4.
CBSE Board UP Board and Others state Board.
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 the bottom rungs are 2(1/2)m apart, what is the length of the wood required for the rungs?
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The distance between top and bottom rungs is 2(1/2)m and the distance between two successive rungs is 25 cm, therefore
The number of rungs = 250/25 + 1 = 11
The lenght of rungs is increasing from 25 cm to 45 cm in the from of AP, whose first term a = 25 and the last term a₁₁ = 45
Let the common difference of this AP be d.
Therefore, a₁₁ = 45
⇒ a + (11 – 1)d = 45
⇒ 25 + 10d = 45
⇒ d = 20/10 = 2
The lenght of wood required
S₁₁ = 11/2[2a + (11 -1)d]
= 11/2[2(25) + 10(2)]
= 11 × 35 = 385 cm
Hence, 385 cm lenght of the wood is required for the rungs.