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?
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Verified answer
Answer:
∴ the total number of rungs.
2 ¹/2×100/25+1
= 250/25+1=11
Now, as the lengths of the rungs decrease uniformly, they will be in an A.P.
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
n=11
Sn=n/2(a+l)
S10=11/2(45+25)=11/2×70=385 cm
Therefore, the length of wood is 385cm
Explanation:
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Answer:
It is given that the rungs are 25 cm apart and the top and bottom rungs are 2
2
1
m apart.
∴ the total number of rungs.
25
2
2
1
×100
+1
=
25
250
+1=11
Now, as the lengths of the rungs decrease uniformly, they will be in an A.P.
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
n=11
S
n
=
2
n
(a+l)
S
10
=
2
11
(45+25)=
2
11
×70=385 cm
Therefore, the length of wood is 385cm