A ladder has rungs 25 , cm apart. (see Figure | vedclass

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(D) The rungs are placed at a distance of $25 \, cm$ from each other. The total distance between the top and bottom rung is $2 \frac{1}{2} \, m = 250

Vedclass · Accepted Answer

$385$

Vedclass · Answer

(D) The rungs are placed at a distance of $25 \, cm$ from each other. The total distance between the top and bottom rung is $2 \frac{1}{2} \, m = 250 \, cm$.The number of gaps between the rungs is $\frac{250}{25} = 10$.Since there is a rung at both ends,the total number of rungs $n$ is $10 + 1 = 11$.As the lengths of the rungs decrease uniformly,they form an Arithmetic Progression $(A.P.)$.The first term $a = 45 \, cm$ and the last term $l = 25 \, cm$.The total length of the wood required is the sum of the $A.P.$ series,given by the formula $S_n = \frac{n}{2}(a + l)$.Substituting the values: $S_{11} = \frac{11}{2}(45 + 25) = \frac{11}{2}(70) = 11 	imes 35 = 385 \, cm$.Thus,the total length of wood required for the rungs is $385 \, cm$.

$A$ ladder has rungs $25 \, cm$ apart. (see Figure). 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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