A ladder has rungs 25 cm. apart. The rungs decrease uniformly in the length from 45 cm. at the bottom to 25 cm. at the top. If the top and the bottom rungs are 221m apart, what is the length of the wood required for the rungs

Question

A ladder has rungs 25 cm. apart. The rungs decrease uniformly in the length from 45 cm. at the bottom to 25 cm. at the top. If the top and the bottom rungs are 221​m apart, what is the length of the wood required for the rungs

Filo · Accepted Answer

The distance between the top and the bottom rungs

= 2 \frac{1}{2}

m

= 250

cm and the distance between two consecutive rungs

= 25

cm.

Therefore, the number of gaps between the rungs

= \frac{250}{25} = 10

.

So, the total number of rungs in the ladder

= 11

The length of the bottom rung is

45

cm and the lengths of rungs decrease uniformly from bottom to top.

Therefore, the numbers involved in the lengths (in cm) of the rungs from bottom to top form an AP with

a = 45, l = 25

and

n =

total number of rungs

= 11

.

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

= \frac{11}{2} \times 70

= 11 \times 35 = 385

Hence, the length of the wood required for rungs

= 385

cm.

Question Text	A ladder has rungs $25$ cm. apart. The rungs decrease uniformly in the 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	150

A ladder has rungs $25$ cm. apart. The rungs decrease uniformly in the 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

Text solutionVerified

Practice questions from similar books

A ladder has rungs 25 cm. apart. The rungs decrease uniformly in the length from 45 cm. at the bottom to 25 cm. at the top. If the top and the bottom rungs are 221​m apart, what is the length of the wood required for the rungs

Text solutionVerified

Practice questions from similar books

A ladder has rungs $25$ cm. apart. The rungs decrease uniformly in the 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