A ladder has rungs 25 cm apart. 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? [Hint: Number of rungs = -250/25 ].
Distance between the rungs of the ladder is 25cm.
Distance between the top rung and bottom rung of the ladder is = \(2\frac{1}{2}\)m = \(2\frac{1}{2}\times 100 cm\) = \(\frac{5}{2}\times 100\)cm
= 250cm
Therefore, total number of rungs = 250/25 + 1 = 11
As we can see from the figure, the ladder has rungs in decreasing order from top to bottom.
First term, a = 45
Last term, l = 25
Number of terms, n = 11
Sn= n/2(a+ l)
Sn= 11/2(45+25)
= 11/2(70) = 385 cm
Hence, the length of the wood required for the rungs is 385cm.