A ladder has rungs 25 cm apart(see below figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 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?
"
Given:
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 at the top.
The top and the bottom rungs are $2\frac{1}{2}\ m$ apart.
To do:
We have to find the length of the wood required for the rungs.
Solution:
The length of the rung at the bottom $a=45\ cm$
The length of the rung at the top $l=25\ cm$
The top and the bottom rungs are $\frac{5}{2}\ m=\frac{500}{2}\ cm=250\ cm$ apart.
Let the number of rungs be $n$
This implies,
Number of rungs $n=\frac{250}{25}+1$
$=11$
Therefore,
The sum of lengths of 11 rungs $S_{n}=\frac{n}{2}(a+l)$
$S_{11}=\frac{11}{2}(45+25)$
$=11(35)$
$=385\ cm$
Hence, the required length of the wood is $385\ cm$.
Related Articles
- A table-top measures \( 2 \mathrm{~m} 25 \mathrm{~cm} \) by \( 1 \mathrm{~m} 50 \mathrm{~cm} \). What is the perimeter of the table-top?
- The radii of the top and bottom of a bucket of slant height $45\ cm$ are $28\ cm$ and $7\ cm$ respectively. Find the curved surface area of the bucket.
- Find the area and perimeter of the rectangle, if length $=46 cm$ and breadth $=25 cm$
- If the areas of three adjacent faces of a cuboid are $8\ cm^2, 18\ cm^2$ and $25\ cm^2$. Find the volume of the cuboid.
- From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20\ m$ high building are $45^o$ and $60^o$ respectively. Find the height of the tower.
- Name the metal which has been placed:(a) At the bottom of the reactivity series (b) At the top of the reactivity series (c) Just below copper in the reactivity ser
- Find the length of the longest tape that can be used to measure the exactly the length 4 m 20 cm, 2 m 40 cm and 3 m 60 cm.
- From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of \( 20 \mathrm{~m} \) high building are \( 45^{\circ} \) and \( 60^{\circ} \) respectively. Find the height of the transimission tower.
- An object 2 cm high is placed at a distance of 14 cm formed below the principal axis that is , it is a real and inverted image:1) what is the focal length of the mirror 2) find the position of the image
- The length of rectangle is $25\ m$ and width of rectangle is $56\ cm$ find the perimeter of rectangle.
- The breadth of a rectangle is 4 cm less than its length if the length is increased by 4 cm and the breadth is decreased by 1 cm, the area of the rectangle is increased by $40\ cm^2$. Find the length and breadth of the rectangle.
- A wooden bookshelf has external dimensions as follows: Height \( =110 \mathrm{~cm} \), Depth \( =25 \mathrm{~cm} \), Breadth \( =85 \mathrm{~cm} \) (see figure below). The thickness of the plank is \( 5 \mathrm{~cm} \) everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per \( \mathrm{cm}^{2} \) and the rate of painting is 10 paise per \( \mathrm{cm}^{2} \), find the total expenses required for polishing and painting the surface of the bookshelf."
- While measuring the length of a knitting needle, the reading of the scale at one end is 3.0 cm and at the other end is 33.1 cm. What is the length of the needle?
- The area of two similar triangles are $25\ cm^2$ and $36\ cm^2$ respectively. If the altitude of the first triangle is $2.4\ cm$, find the corresponding altitude of the other.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
To Continue Learning Please Login