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 botom rungs are two nd a half metre apart, what is the length of the wood required for the rungs
The number of rungs is eleven. Measured from the bottom rung up, their vertical distances are 0, 0.25, 0.50, 0.75, 1.0. 1.25, 1.50, 1.75, 2.00, 2.25 and 2.50 meters. Rung length increases from 45 at the bottom to 25 at the top, so rung lengths are:
45, 43, 41, 39, 37, 35, 33, 31, 29, 27 and 25 cm.
Add up those numbers for wood length required. Looks like 11 x 35 = 385 cm
To find the length of wood required for the rungs, we need to determine the number of rungs on the ladder and then calculate the total length.
First, let's find the number of rungs on the ladder. Given that the ladder has rungs 25 cm apart and the top and bottom rungs are two and a half meters (250 cm) apart, we can find the number of rungs by dividing the total distance by the distance between each rung:
Number of rungs = Total distance / Distance between each rung
Number of rungs = 250 cm / 25 cm
Number of rungs = 10
Therefore, there are 10 rungs on the ladder.
Now, let's calculate the total length of wood required for the rungs. Since the rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top, we can find the average length of the rungs and then multiply it by the number of rungs:
Average length of rungs = (45 cm + 25 cm) / 2
Average length of rungs = 70 cm / 2
Average length of rungs = 35 cm
Total length of wood required = Average length of rungs x Number of rungs
Total length of wood required = 35 cm x 10
Total length of wood required = 350 cm
Therefore, the length of wood required for the rungs is 350 cm.