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A ladder has rungs 25 cm apart(see below figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 at the top. If the top and the bottom rungs are $2\frac{1}{2}\ m$ apart, what is the length of the wood required for the rungs?
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Given:

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 at the top.

The top and the bottom rungs are $2\frac{1}{2}\ m$ apart.
To do:

We have to find the length of the wood required for the rungs.

Solution:

The length of the rung at the bottom $a=45\ cm$

The length of the rung at the top $l=25\ cm$

The top and the bottom rungs are $\frac{5}{2}\ m=\frac{500}{2}\ cm=250\ cm$ apart.

Let the number of rungs be $n$

This implies,

Number of rungs $n=\frac{250}{25}+1$

$=11$

Therefore,

The sum of lengths of 11 rungs $S_{n}=\frac{n}{2}(a+l)$

$S_{11}=\frac{11}{2}(45+25)$

$=11(35)$

$=385\ cm$

Hence, the required length of the wood is $385\ cm$.

Updated on: 10-Oct-2022

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