Question

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 $2\frac{1}{2}m$ apart, what is the length of the wood required for the rungs

Answer 1

It is given that the rungs are $25$ cm apart and the top and bottom rungs are $2\frac{1}{2}$ m apart.

$\therefore$ the total number of rungs.

$\frac{2\frac{1}{2}\times 100}{25}+1$

$=$ $\frac{250}{25}+1=11$

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, $l=25$

$n=11$

$S_n=\frac{n}{2}(a+l)$

$S_{10}=\frac{11}{2}(45+25)=\frac{11}{2}\times 70=385$ cm

Therefore, the length of wood is $385$cm