Question

A carpenter wants to manufacture a 3 metre ladder having rungs 25 cm apart. The rungs decreases uniformly in length from 45 cm at the bottom at 25 cm at the top and the top and bottom rungs are 2.5 metre apart.
Based on the above information answer the following questions :
(i) Total number of rungs in the ladder.
(ii) The lengths of rungs from bottom to top form an A.P. with first and last terms as 45 cm and 25 cm respectively. The common difference of the A.P. formed.
(iii) The length of the middle rung.
(iv) Length of the wood used for rungs.
(v) length of wood required for the ladder.

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Answer 1

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Distance between the starting rung and the top most rung = 250 cm

Number of rungs in 250 cm with spacing of 25 cm = 250/25 = 10

Including the bottom most rung the total number of rungs on the ladder = 11

The length of rungs is an Arithmetic progression/series.

Sum of lengths of all 11 rungs = (1st term + last term)/2 * number of rungs

= (45+25)/2 * 11 = 385 cm

Step-by-step explanation:

Solution :-

It is given that the top and bottom rungs are 250 cm apart and the gaps between two consecutive rungs is 25 cm.

Therefore,

Number of rungs = (250/25 + 1) = 11

The largest rung is 45 cm long and the smallest one is 25 cm long.

It is given that the rungs are decreasing uniformly in length from 45 cm at the bottom to 25 cm at the top.

So, the lengths of the rungs from an A.P. with a = 45 cm and l = length of 11th rung = 25 cm.

Therefore,

Length of the wood required to form 11 rungs

= n/2 (a + l) cm

= 11/2(45 + 25) cm

= 11/2 × 70

= 385 cm.

Hence, the required length of the wood to form these rungs is 3.85 m

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Answer 2

Answer:

1. 11rungs

2.d= -2cm

3. 35cm

4. 385cm / 3.85m

5. 985cm /9.85m

Step-by-step explanation:

1. distance between top and bottom rungs is 250cm and distance between any two consequent rungs is 25cm .

therefore, 250/25= 10

10+1 (bottom rung to be added as it was not counted)=11rungs

2. length of the rungs=45,...........,25

n=11rungs

last term can be taken as an
an=a+(n-1)d
25=45+10d
d=-2cm

3. given: a=45cm
proved: n=11(rungs)

middle rung = 11+1/2=6th rung

an=a+(n-1)d
a6=45+(5*-2)

a6=35cm

4. length of wood used for rungs

sum of all the length of rungs

Sn=n/2(a+l)                 l=last term

S11= 11/2(45+25

S11=385cm

5. length of wood required in total

given : ladder total height is 3m so either side supports in total make 6m plus the rungs

so , 3.85m+3m+3m=9.85m