Aladder is leaning against a wall. the top of the ladder touches the wall at a height that is 5 feet less than the length of the ladder. the distance from the foot of the ladder to the wall is 10 feet less than the length of the ladder. how long is the ladder?

25 feet

Explanation:

Let the ladder be 'H' feet long

Given;

Ladder touches the wall at a height = H - 5 feet

The distance from the foot of the ladder to the wall = H - 10 feet

now a right angles triangle is formed by the system,

where,

Ladder forms the hypotenuse of the triangle

Height of the wall is the perpendicular

and, distance at the base is the base of the triangle formed

Therefore,

from the Pythagoras theorem, we have

H² = ( H - 10 )² + ( H - 5 )²

or

H² = H² + 100 - 20H + H² + 25 - 10H

or

H² = 2H² + 125 - 30H

or

H² -30H + 125 = 0

on solving the quadratic equation, we get

H² + ( - 5H - 25H ) + 125 = 0

or

H ( H - 5 ) - 25 (H - 5) = 0

or

(H - 5) × (H - 25) = 0

therefore,

we have

H = 5 feet and H = 25 feet

now,

H = 5 is not possible as this length of the ladder will lead to the negative distance at the base and also, the height of the at the wall be zero

Hence,

the length of the ladder is 25 feet

modern day technological advancements are constantly seen throughout every aspect of life. cell phones, portable internet availability, laptop computers, ipods, mp3 players of every brand, and many other devices, are everywhere. they seem to possess unending possible detriments, but, along with such issues, technology also has positive impacts on today’s youth. in some situations, the internet and ipod prevent sociability, though in others they may be the cause of increased social activity. overall, modern technology has the capability to bring people together as well as enhance the social abilities of the today’s youth; however, if used without discretion, can also create a less interactive generation, frequently depending on technology for contentment.  

the immense capabilities of the internet today are astonishing, and offer many positive opportunities for teens. primarily, the internet makes sharing information fast and simple, despite factors that in other cases would prohibit such simple distribution. according to jean-francois coget in source c, “with the internet, information can be transmitted and received with ease at any time of the day to and from any number of friends.” it is possible to send videos, pictures, papers, projects, and a quantity of other things with the click of a button. the transfer can happen in seconds. the amazing capability of modern day internet simplifies teenage life, by providing a way to convey knowledge. another way in which internet proves positive is by providing a way to keep in touch with friends and family worldwide, or just across town. whether it’s a friend that switched schools and is never around, or a family member in london, the internet makes it possible to email, instant message, and even video chat. such qualities of internet communication bring people together with more frequent contact, boosting sociability and relationships. in addition, the internet also has the capability to, “foster openness, self-confidence, and a greater sense of ease, and comfort in dealing with others” (source c). since it is not obligatory to reveal physical appearance or social status over the internet, it grants an opportunity to be a completely new person, who is entirely open and confident. internet chats, even with mere acquaintances, can supply a chance for socially challenged teens to experience a form of social interaction, in order to create a sense of composure. modern day internet advancements not only offer an easier way to share information, but also contribute to sociability by providing a way to communicate with distant friends and family, as well as giving socially challenged teenagers an opportunity for interaction.

likewise, another modern day technology, the ipod, may also have a positive effect on some teenagers, by presenting a different view of the world as well as uniting individuals through musical taste. in the eyes of kelly doyle-mace, in source d, “music deepens the experience of walking through the world, rather than detracting from it.” there are millions of songs out there, one to match every possible mood. sometimes, turning on just the right song can be motivational and provide a completely new outlook on a certain circumstance. in addition, lyrics are often relatable to personal life and can be significant or simply encouraging. another way in which ipods and personal musical taste is a positive effect on teens is by uniting people of different backgrounds and diversities through their music choice. lisa and johnny rocket, hosts of “ipod dj nights,” describe that one night a month they invite guests to bring their ipods to a london bar. where they can play whatever songs they choose (source d). “even more diverse than the music are the members… the ipod acts to bring people together,” lisa explains (source d). these gatherings prove that as diverse as music can be, it is also unifying. the multitudes of people attending these parties, from every race background and belief, are united through their assorted music taste. ipods have the potential to positively affect today’s youth by matching any and every mood with music, resulting in a deeper walk through life, as well as bringing people together by means of musical interest.

the alternative argument is that the internet can be a significantly negative influence on teenagers, if overused. constant internet use detracts time that could be spent with friends and family. hours wasted away typing useless messages is detrimental to personal relationships with the ones who really matter. it was discovered through a study in pittsburgh that people who use the internet most often are “spending less time talking with their families…keeping up with fewer friends” (source b). it is of no use to spend so much time talking to people over the internet, when one could just as easily walk down the stairs and spend time with family, or go to see friends instead. according to source

1, 4, and 5 are all conflicts