Question

a ladder has rungs 25cm apart. the rungs decrease uniformly in length from 45cm at the bottom to 25cm at the top. if the top and bottom rungs are 5/2m
apart, what is the length of the woods required for the rungs?
$(hint:number \: of \: rungs \: = \frac{250}{25} + 11)$

Answer 1

Here is your solution

Let,

The first term = a = 0

d= common difference =25 cm=0.25m.

When the rungs are measured from top to bottom , then the 

0, 0.25, 0.50, 0.75, 1.0. 1.25, 1.50, 1.75, 2.00, 2.25 and 2.50 metres.

=>The number of rungs is eleven.

Now, 

Rung length decreases 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. 

If the top and the bottom rungs are two and a half metre apart,then

The length of the wood required for the rungs= 11 x 35 = 385 cm.

I hope it helps you

Answer 2

Here is your answer

$\bold{\purple{\boxed{\boxed{\huge\underline{Solution}}}}}$


DISTANCE BETWEEN FIRST AND LAST RUNGS=2.5M=250CM

DISTANCE BETWEEN FIRST AND SECOND RUNGS=25CM

NUMBER OF RUNGS=250/25+1=11 RUNGS

So length of wood = Sn = n/2 (a + l )

  =11/2 (45+25 )

  =11/2 (70)

  =385 cm