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Home » A ladder has rungs 25 cm apart. (see Fig. 5.7). 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 apart, what is the length of the wood required for the rungs? [Hint: Number of rungs = -250/25 ].
A ladder has rungs 25 cm apart. (see Fig. 5.7). 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 apart, what is the length of the wood required for the rungs? [Hint: Number of rungs = -250/25 ].
Arithmetic Progression | CBSE | Class 10 | Maths | NCERT
A ladder has rungs 25 cm apart. (see Fig. 5.7). 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 apart, what is the length of the wood required for the rungs? [Hint: Number of rungs = -250/25 ].

Solution:

Given,

The ladder has a 25cm distance between the rungs.

The distance between the ladder’s top and bottom rungs of ladder is

=2\frac{1}{2}m=2\frac{1}{2}*100cm
= 5/2 ×100cm

= 250cm

As a result, the total number of rungs is 250/25 + 1 = 11

The rungs on the ladder are arranged in decreasing sequence from top to bottom, as shown in the diagram. As a result, we can deduce that the rungs are decreasing in order of AP.

The length of wood needed for the rungs will be equal to the sum of the AP series terms created.

So,

The first term, a = 45

The last term, l = 25

Number of terms, n = 11

As we all know, the sum of nth terms equals to

Sn= n/2(a+ l)

Sn= 11/2(45+25) = 11/2(70) = 385 cm

As a result, 385cm of wood is required for the rungs.

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