A ladder has rungs 25 cm apart. The rungs decrease uniformly from 60 cm at bottom to 40 cm at top. If the distance between the top ring and the bottom rung is 2.5 m, find the length of the wood required.
Answers
Dear student,
Answer : Length of wood required is 500 cm.
Solution:
ATQ
Number of rungs n = 2.5(100)/25 = 10
(∴ distance is given in meters, so multiply by 100)
From the formula of AP: Sum of AP when 1st and last term are given.
here first term a = 60 ( i.e. bottom rung)
last term is l = 40 (i.e. top rung)
Sum of all Rungs = n/2( a + l)
= 10/2 ( 60+40)
= 5(100)
= 500 cm
so, length of wood required is 500 cm
Hope it helps you.
Given Distance between two consecutive rungs = 25 cm.
Given that the distance between the top rung and bottom rung = 2.5 m
= > 2.5 * 100 cm
= > 250 cm
Now,
We know that Number of rungs = (Total length/Distance between rungs) + 1
= > (250/25) + 1
= > 11.
Given that the length of the first run = 60 cm.
Given that the length of second rung = 40 cm.
Sum of lengths of 11 rungs = (11/2)[60 + 40]
= > 11/2[100]
= > 11 * 50
= > 550cm
= > 5.5 metres.
Therefore, the length of wood required = 550 cm.
Hope this helps!
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