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 the bottom rungs are $2.5 m$ apart, what is the length of the wood required for the rungs?

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Solution

$\begin{matrix} G i v e n, D i s tan c e b e t w e e n t w o r u n g s = 25 c m T o t a l l e n g t h = 2.5 m = 250 c m N o . o f r u n g s = \frac{t o t a l l e n g t h}{d i s tan c e b e t w e e n 2 r u n g s} = \frac{250}{25} + 1 = 11 H e r e, l e n g t h o f t h e r u n g s i n c r e s e s f r o m 25 c m t o 45 c m . s o, A . P i s 25, . . . . . ., 45, w h i c h h a v e 11 t e r m s i n t o t a l . T o t a l w o o d r e q u i r e d = s u m o f A . P s = \frac{n}{2} (a + l) = \frac{11}{2} (45 + 25) = 358 c m H e n c e, L e n g t h o f w o o d r e q u i r e d i s 385 c m . \end{matrix}$

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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 the bottom rungs are $2.5 m$ apart, what is the length of the wood required for the rungs?