Optimization: page margins and ladder length

[Baps]

Question #1
A printed page will have margins of 2 cm at the top and sides and 4 cm at the bottom. If the printed area is 150cm squared, find the dimentions of the whole page so that its area will be a minimum.

Question #2
Painters are painting the second floor exterior wall of the building that adjoins a busy sidewalk. A corridor 2m wide and 3 m high is built to protect pedestrians. What is the length of the shortest ladder that will reach from the ground over the corridor of the wall of the building?

 

[griffon]

Ooh! Someone please answer this one. I have the same problems only with different numbers.

 

[vaishakh]

i request to use calculus. take length as x-6. then solve for breadth dor he equation. report if you don't get after two days.

 

[HallsofIvy]

Have you done ANYTHING except just copy the problem down?

1) Since you are asked for the dimensions of the page, let x= length, y= width of the page. What are the dimensions of the printed area?

2) Draw a picture! Draw the corridor, seen from the end, as rectangle and draw the ladder just touching the outer corner. Do you see that the ladder forms the hypotenuse of a right triangle?