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A ladder has rungs 25 cm apart. The rungs decrease uniformly i

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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

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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

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Text solutionVerified

It is given that the rungs are

25

cm apart and the top and bottom rungs are

2 \frac{1}{2}

m apart.

∴

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

Therefore, the length of wood is

385

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Question Text	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 Type	Text solution:1
Upvotes	151